lib/dotgen/aspect.c

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/* $Id$ $Revision$ */
/* vim:set shiftwidth=4 ts=8: */

/*************************************************************************
 * Copyright (c) 2011 AT&T Intellectual Property 
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * http://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: See CVS logs. Details at http://www.graphviz.org/
 *************************************************************************/

#include "dot.h"

/*
 * Author: Mohammad T. Irfan
 *   Summer, 2008
 */

/* TODO:
 *   - Support clusters
 *   - Support disconnected graphs
 *   - Provide algorithms for aspect ratios < 1
 */

#define DPI 72

/*
 *       NODE GROUPS FOR SAME RANKING
 *       Node group data structure groups nodes together for
 *       MIN, MAX, SOURCE, SINK constraints.
 *       The grouping is based on the union-find data structure and
 *       provides sequential access to the nodes in the same group.
 */

/* data structure for node groups */
typedef struct nodeGroup_t {
    node_t **nodes;
    int nNodes;
    double width, height;
} nodeGroup_t;

static nodeGroup_t *nodeGroups;
static int nNodeGroups = 0;

/* computeNodeGroups:
 * computeNodeGroups function does the groupings of nodes.   
 * The grouping is based on the union-find data structure.
 */
static void computeNodeGroups(graph_t * g)
{
    node_t *n;

    nodeGroups = N_GNEW(agnnodes(g), nodeGroup_t);

    nNodeGroups = 0;

    /* initialize node ids. Id of a node is used as an index to the group. */
    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        ND_id(n) = -1;
    }

    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        if (ND_UF_size(n) == 0) {       /* no same ranking constraint */
            nodeGroups[nNodeGroups].nodes = NEW(node_t *);
            nodeGroups[nNodeGroups].nodes[0] = n;
            nodeGroups[nNodeGroups].nNodes = 1;
            nodeGroups[nNodeGroups].width = ND_width(n);
            nodeGroups[nNodeGroups].height = ND_height(n);

            ND_id(n) = nNodeGroups;
            nNodeGroups++;
        } else                  /* group same ranked nodes */
        {
            node_t *l = UF_find(n);
            if (ND_id(l) > -1)  /* leader is already grouped */
            {
                int index = ND_id(l);
                nodeGroups[index].nodes[nodeGroups[index].nNodes++] = n;
                nodeGroups[index].width += ND_width(n);
                nodeGroups[index].height =
                    (nodeGroups[index].height <
                     ND_height(n)) ? ND_height(n) : nodeGroups[index].
                    height;

                ND_id(n) = index;
            } else              /* create a new group */
            {
                nodeGroups[nNodeGroups].nodes =
                    N_NEW(ND_UF_size(l), node_t *);

                if (l == n)     /* node n is the leader */
                {
                    nodeGroups[nNodeGroups].nodes[0] = l;
                    nodeGroups[nNodeGroups].nNodes = 1;
                    nodeGroups[nNodeGroups].width = ND_width(l);
                    nodeGroups[nNodeGroups].height = ND_height(l);
                } else {
                    nodeGroups[nNodeGroups].nodes[0] = l;
                    nodeGroups[nNodeGroups].nodes[1] = n;
                    nodeGroups[nNodeGroups].nNodes = 2;
                    nodeGroups[nNodeGroups].width =
                        ND_width(l) + ND_width(n);
                    nodeGroups[nNodeGroups].height =
                        (ND_height(l) <
                         ND_height(n)) ? ND_height(n) : ND_height(l);
                }

                ND_id(l) = nNodeGroups;
                ND_id(n) = nNodeGroups;
                nNodeGroups++;
            }
        }
    }

}

/*
 *       END OF CODES FOR NODE GROUPS 
 */

/* countDummyNodes:
 *  Count the number of dummy nodes
 */
int countDummyNodes(graph_t * g)
{
    int count = 0;
    node_t *n;
    edge_t *e;

    /* Count dummy nodes */
    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        for (e = agfstout(g, n); e; e = agnxtout(g, e)) {
#ifdef UNUSED
            /* this loop can be avoided */
            for (k = ND_rank(agtail(e))+1; k < ND_rank(aghead(e)); k++) {
               count++;
            }
#endif
                /* flat edges do not have dummy nodes */
            if (ND_rank(aghead(e)) != ND_rank(agtail(e)))       
                count += abs(ND_rank(aghead(e)) - ND_rank(agtail(e))) - 1;
        }
    }
    return count;
}

/*
 *       FFDH PACKING ALGORITHM TO ACHIEVE TARGET ASPECT RATIO
 */

/*
 *  layerWidthInfo_t: data structure for keeping layer width information
 *  Each layer consists of a number of node groups.
 */
typedef struct layerWidthInfo_t {
    int layerNumber;
    nodeGroup_t **nodeGroupsInLayer;
    int *removed;               /* is the node group removed? */
    int nNodeGroupsInLayer;
    int nDummyNodes;
    double width;
    double height;
} layerWidthInfo_t;

static layerWidthInfo_t *layerWidthInfo = NULL;
static int *sortedLayerIndex;
static int nLayers = 0;

/* computeLayerWidths:
 */
static void computeLayerWidths(graph_t * g)
{
    int i;
    node_t *v;
    node_t *n;
    edge_t *e;

    nLayers = 0;

    /* free previously allocated memory */
    if (layerWidthInfo) {
        for (i = 0; i < nNodeGroups; i++) {
            if (layerWidthInfo[i].nodeGroupsInLayer) {
                int j;
                for (j = 0; j < layerWidthInfo[i].nNodeGroupsInLayer; j++) {
                    //if (layerWidthInfo[i].nodeGroupsInLayer[j])
                    //free(layerWidthInfo[i].nodeGroupsInLayer[j]);
                }
                free(layerWidthInfo[i].nodeGroupsInLayer);
            }
            if (layerWidthInfo[i].removed)
                free(layerWidthInfo[i].removed);
        }

        free(layerWidthInfo);
    }
    /* allocate memory
     * the number of layers can go up to the number of node groups
     */
    layerWidthInfo = N_NEW(nNodeGroups, layerWidthInfo_t);

    for (i = 0; i < nNodeGroups; i++) {
        layerWidthInfo[i].nodeGroupsInLayer =
            N_NEW(nNodeGroups, nodeGroup_t *);

        layerWidthInfo[i].removed = N_NEW(nNodeGroups, int);

        layerWidthInfo[i].layerNumber = i;
        layerWidthInfo[i].nNodeGroupsInLayer = 0;
        layerWidthInfo[i].nDummyNodes = 0;
        layerWidthInfo[i].width = 0.0;
        layerWidthInfo[i].height = 0.0;
    }



    /* Count dummy nodes in the layer */
    for (n = agfstnode(g); n; n = agnxtnode(g, n))
        for (e = agfstout(g, n); e; e = agnxtout(g, e)) {
            int k;

            /* FIX: This loop maybe unnecessary, but removing it and using 
             * the commented codes next, gives a segmentation fault. I 
             * forgot the reason why.
             */
            for (k = ND_rank(agtail(e)) + 1; k < ND_rank(aghead(e)); k++) {
                layerWidthInfo[k].nDummyNodes++;
            }

#ifdef UNUSED
            if (ND_rank(aghead(e)) != ND_rank(agtail(e)))
                /* flat edges do not have dummy nodes  */
                layerWidthInfo[k].nDummyNodes = abs(ND_rank(aghead(e)) - ND_rank(agtail(e))) - 1;
#endif
        }

#ifdef UNUSED
  /*****************************************************************
   * This code is removed. It considers dummy nodes in layer width,
   * which does not give good results in experiments.
   *****************************************************************/

    for (i = 0; i < nNodeGroups; i++) {
       v = nodeGroups[i].nodes[0];
       layerWidthInfo[ND_rank(v)].width = (layerWidthInfo[ND_rank(v)].nDummyNodes - 1) * GD_nodesep(g); 
       }
#endif

    /* gather the layer information */
    for (i = 0; i < nNodeGroups; i++) {
        v = nodeGroups[i].nodes[0];
        if (ND_rank(v) + 1 > nLayers)   /* update the number of layers */
            nLayers = ND_rank(v) + 1;

        layerWidthInfo[ND_rank(v)].width +=
            nodeGroups[i].width * DPI + (layerWidthInfo[ND_rank(v)].width >
                                         0) * GD_nodesep(g);
        if (layerWidthInfo[ND_rank(v)].height < nodeGroups[i].height * DPI)
            layerWidthInfo[ND_rank(v)].height = nodeGroups[i].height * DPI;
        layerWidthInfo[ND_rank(v)].
            nodeGroupsInLayer[layerWidthInfo[ND_rank(v)].
                              nNodeGroupsInLayer] = &nodeGroups[i];
        layerWidthInfo[ND_rank(v)].nNodeGroupsInLayer++;
    }

}

/* compFunction:
 * Comparison function to be used in qsort.
 * For sorting the layers by nonincreasing width
 */
static int compFunction(const void *a, const void *b)
{
    int *ind1 = (int *) a;
    int *ind2 = (int *) b;

    return (layerWidthInfo[*ind2].width >
            layerWidthInfo[*ind1].width) - (layerWidthInfo[*ind2].width <
                                            layerWidthInfo[*ind1].width);
}

/* sortLayers:
 * Sort the layers by width (nonincreasing order)
 * qsort should be replaced by insertion sort for better performance.
 * (layers are "almost" sorted during iterations)
 */
static void sortLayers(graph_t * g)
{
    qsort(sortedLayerIndex, agnnodes(g), sizeof(int), compFunction);
}

#ifdef UNUSED
/* getMaxDummyNodes:
 * get the max # of dummy nodes on the incoming edges to a nodeGroup
 */
static int getMaxDummyNodes(nodeGroup_t * ng)
{
    int i, max = 0, cnt = 0;
    for (i = 0; i < ng->nNodes; i++) {
        node_t *n = ng->nodes[i];
        edge_t *e;
        graph_t *g = agraphof(n);
        for (e = agfstin(g, n); e; e = agnxtin(g, e)) {
            cnt += ND_rank(aghead(e)) - ND_rank(agtail(e));     // it's 1 more than the original count
            if (ND_rank(aghead(e)) - ND_rank(agtail(e)) > max)
                max = ND_rank(aghead(e)) - ND_rank(agtail(e));
        }
    }

    return max;
}
#endif

/* getOutDegree:
 * Return the sum of out degrees of the nodes in a node group.
 */
static int getOutDegree(nodeGroup_t * ng)
{
    int i, cnt = 0;
    for (i = 0; i < ng->nNodes; i++) {
        node_t *n = ng->nodes[i];
        edge_t *e;
        graph_t *g = agraphof(n);

        /* count outdegree. This loop might be unnecessary. */
        for (e = agfstout(g, n); e; e = agnxtout(g, e)) {
            cnt++;
        }
    }

    return cnt;
}

/* compFunction2:
 * Comparison function to be used in qsort.
 * For sorting the node groups by their out degrees (nondecreasing)
 */
static int compFunction2(const void *a, const void *b)
{
    nodeGroup_t **ind1 = (nodeGroup_t **) a, **ind2 = (nodeGroup_t **) b;

    int cnt1 = getOutDegree(*ind1);
    int cnt2 = getOutDegree(*ind2);

    return (cnt2 < cnt1) - (cnt2 > cnt1);
}

#ifdef UNUSED
/* compFunction3:
 * Comparison function to be used in qsort.
 * For sorting the node groups by their height & width
 */
static int compFunction3(const void *a, const void *b)
{
    nodeGroup_t **ind1 = (nodeGroup_t **) a, **ind2 = (nodeGroup_t **) b;
    if ((*ind2)->height == (*ind1)->height)
        return ((*ind2)->width < (*ind1)->width) - ((*ind2)->width >
                                                    (*ind1)->width);

    return ((*ind2)->height < (*ind1)->height) - ((*ind2)->height >
                                                  (*ind1)->height);
}

/*****************************************************************
 * The following commented codes are no longer used
 * Originally used in the cocktail tool.
 *****************************************************************/
/* checkLayerConstraints:
 * check if there is any node group in the layer 
 * that is not constrained by MIN/MAX/SOURCE/SINK-RANK constraints.
 */
static int checkLayerConstraints(layerWidthInfo_t lwi)
{
    int i;
    for (i = 0; i < lwi.nNodeGroupsInLayer; i++) {
        if (lwi.nodeGroupsInLayer[i]->nNodes > 0) {
            int rtype = ND_ranktype(lwi.nodeGroupsInLayer[i]->nodes[0]);
            if (rtype != MINRANK && rtype != MAXRANK && rtype != SOURCERANK
                && rtype != SINKRANK)
                return 1;
        }
    }

    return 0;
}

/* checkLayerConstraints:
 * check if all the node groups in the layer are 
 * constrained by MIN/MAX/SOURCE/SINK-RANK constraints
 */
static int checkLayerConstraints(layerWidthInfo_t lwi)
{
    int i;
    for (i = 0; i < lwi.nNodeGroupsInLayer; i++) {
        if (lwi.nodeGroupsInLayer[i]->nNodes > 0) {
            int rtype = ND_ranktype(lwi.nodeGroupsInLayer[i]->nodes[0]);
            if (rtype != MINRANK && rtype != MAXRANK && rtype != SOURCERANK
                && rtype != SINKRANK)
                return 0;
        }
    }

    return 1;
}

/* checkNodeGroupConstraints:
 * check if the node group is not constrained by 
 * MIN/MAX/SOURCE/SINK-RANK constraints
 * Only used in the cocktail tool.
 */
static int checkNodeGroupConstraints(nodeGroup_t * ndg)
{
    int i;
    int rtype = ND_ranktype(ndg->nodes[0]);

    if (rtype != MINRANK && rtype != MAXRANK && rtype != SOURCERANK
        && rtype != SINKRANK)
        return 1;

    return 0;
}

/* checkHorizontalEdge:
 * check if there is an edge from ng to a node in 
 * layerWidthInfo[nextLayerIndex].
 * Only used in the cocktail tool.
 */
static int
checkHorizontalEdge(graph_t * g, nodeGroup_t * ng, int nextLayerIndex)
{
    int i;
    edge_t *e;

    for (i = 0; i < ng->nNodes; i++) {
        for (e = agfstout(g, ng->nodes[i]); e; e = agnxtout(g, e)) {
            if (layerWidthInfo[nextLayerIndex].layerNumber ==
                ND_rank(aghead(e))) {
                return 1;
            }
        }
    }


    return 0;
}

/* hasMaxOrSinkNodes:
 * check if the the layer lwi has MAX or SINK nodes
 * Only used in the cocktail tool.
 */
static int hasMaxOrSinkNodes(layerWidthInfo_t * lwi)
{
    int i, j;

    for (i = 0; i < lwi->nNodeGroupsInLayer; i++) {
        if (lwi->removed[i])
            continue;
        for (j = 0; j < lwi->nodeGroupsInLayer[i]->nNodes; j++) {
            if (ND_ranktype(lwi->nodeGroupsInLayer[i]->nodes[j]) == MAXRANK
                || ND_ranktype(lwi->nodeGroupsInLayer[i]->nodes[j]) ==
                SINKRANK)
                return 1;
        }
    }

    return 0;
}

/* reduceMaxWidth:
 * The following function is no longer used.
 * Originally used for FFDH packing heuristic
 * FFDH procedure
 */
static void reduceMaxWidth(graph_t * g)
{
    int i;
    int maxLayerIndex;          // = sortedLayerIndex[0];
    double nextMaxWidth;        // = (nLayers > 1) ? layerWidthInfo[sortedLayerIndex[1]].width : 0;
    double w = 0;
    Agnode_t *v;

    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[sortedLayerIndex[i]].nNodeGroupsInLayer <= 1)        // || !checkLayerConstraints(layerWidthInfo[sortedLayerIndex[i]]))
            continue;
        else {
            maxLayerIndex = sortedLayerIndex[i];
            nextMaxWidth =
                (nLayers >
                 i + 1) ? layerWidthInfo[sortedLayerIndex[i +
                                                          1]].width : 0;
            break;
        }
    }

    if (i == nLayers)
        return;                 //reduction of layerwidth is not possible.


    //sort the node groups in maxLayerIndex layer by height and then width, nonincreasing
    qsort(layerWidthInfo[maxLayerIndex].nodeGroupsInLayer,
          layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer,
          sizeof(nodeGroup_t *), compFunction2);
    //printf("ht0 = %lf, ht1 = %lf\n", ND_height(layerWidthInfo[maxLayerIndex].nodes[0]), ND_height(layerWidthInfo[maxLayerIndex].nodes[1]));


    if (nextMaxWidth <= layerWidthInfo[maxLayerIndex].width / 2
        || nextMaxWidth == layerWidthInfo[maxLayerIndex].width)
        nextMaxWidth = layerWidthInfo[maxLayerIndex].width / 2;

    double targetWidth = nextMaxWidth;  //layerWidthInfo[maxLayerIndex].width/2;

    //printf("max = %lf, target = %lf\n", layerWidthInfo[maxLayerIndex].width, targetWidth);//,  w + (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->width );
    //getchar();


    //packing by node demotion
    int nextLayerIndex = -1;
    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[i].layerNumber ==
            layerWidthInfo[maxLayerIndex].layerNumber + 1)
            nextLayerIndex = i;
    }

    if (nextLayerIndex > -1) {
        //if (layerWidthInfo[nextLayerIndex].width <= 0.5*layerWidthInfo[maxLayerIndex].width)
        //{
        int changed = 0;
        //demote nodes to the next layer
        for (i = 0; i < layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer;
             i++) {
            if (layerWidthInfo[maxLayerIndex].removed[i])
                continue;

            if (!checkHorizontalEdge
                (g, layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i],
                 nextLayerIndex)
                && w + layerWidthInfo[nextLayerIndex].width +
                (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->
                width <= targetWidth) {
                w += (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->
                    width;
                changed++;

                int j;
                nodeGroup_t *ng =
                    layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i];

                layerWidthInfo[maxLayerIndex].removed[i] = 1;
                layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer--;
                layerWidthInfo[maxLayerIndex].width -= ng->width;
                for (j = 0; j < ng->nNodes; j++)
                    ND_rank(ng->nodes[j])++;


                layerWidthInfo[nextLayerIndex].
                    nodeGroupsInLayer[layerWidthInfo[nextLayerIndex].
                                      nNodeGroupsInLayer] = ng;
                layerWidthInfo[nextLayerIndex].
                    removed[layerWidthInfo[nextLayerIndex].
                            nNodeGroupsInLayer] = 0;
                layerWidthInfo[nextLayerIndex].nNodeGroupsInLayer++;
                layerWidthInfo[nextLayerIndex].width += ng->width;

                //int jj;
                //for (jj = 0; jj < layerWidthInfo[nextLayerIndex].nNodeGroupsInLayer; jj++) {
                    //Agnode_t *node = layerWidthInfo[nextLayerIndex].nodeGroupsInLayer[jj]->nodes[0];
                    //printf("%s\n", agnameof(node));
                //}
            }

        }

        if (changed) {
            //printf("Demoted %d nodes\n", changed);
            return;
        }
        //}
    }
    //packing by creating new layers. Must be commented out if packing by demotion is used

    //going to create a new layer. increase the rank of all higher ranked nodes. (to be modified...)
    for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
        if (ND_rank(v) > layerWidthInfo[maxLayerIndex].layerNumber)     
            ND_rank(v)++;
    }

    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[i].layerNumber >
            layerWidthInfo[maxLayerIndex].layerNumber)
            layerWidthInfo[i].layerNumber++;
    }

    //now partition the current layer into two layers (to be modified to support general case of > 2 layers)
    int flag = 0;               //is a new layer created?
    int alt = 0;
    for (i = 0; i < layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer; i++) {
        if (layerWidthInfo[maxLayerIndex].removed[i])
            continue;

        //nodesep-> only if there are > 1 nodes*******************************
        if ((w +
             (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->width *
             DPI + (w > 0) * GD_nodesep(g) <= targetWidth && alt == 0
             && ND_ranktype(layerWidthInfo[maxLayerIndex].
                            nodeGroupsInLayer[i]->nodes[0]) != SINKRANK
             && ND_ranktype(layerWidthInfo[maxLayerIndex].
                            nodeGroupsInLayer[i]->nodes[0]) != MAXRANK)
            ||
            (ND_ranktype
             (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i]->
              nodes[0]) != SINKRANK
             && ND_ranktype(layerWidthInfo[maxLayerIndex].
                            nodeGroupsInLayer[i]->nodes[0]) != MAXRANK
             && hasMaxOrSinkNodes(&layerWidthInfo[maxLayerIndex]))
            )
            //&& ND_pinned(layerWidthInfo[maxLayerIndex].nodes[i]) == 0 ) 
        {
            w += (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->
                width * DPI + (w > 0) * GD_nodesep(g);
            alt = 1;
        } else {
            int j;
            nodeGroup_t *ng =
                layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i];

            flag = 1;

            layerWidthInfo[maxLayerIndex].removed[i] = 1;
            layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer--;
            layerWidthInfo[maxLayerIndex].nDummyNodes++;        
            layerWidthInfo[maxLayerIndex].width -=
                (ng->width * DPI + GD_nodesep(g));
            for (j = 0; j < ng->nNodes; j++)
                ND_rank(ng->nodes[j])++;

            //create new layer
            layerWidthInfo[nLayers].
                nodeGroupsInLayer[layerWidthInfo[nLayers].
                                  nNodeGroupsInLayer] = ng;
            layerWidthInfo[nLayers].nNodeGroupsInLayer++;
            layerWidthInfo[nLayers].layerNumber = ND_rank(ng->nodes[0]);

            layerWidthInfo[nLayers].width += (ng->width * DPI + (layerWidthInfo[nLayers].nNodeGroupsInLayer > 1) * GD_nodesep(g));      // just add the node widths now. 

            alt = 0;
        }
    }

    if (flag) {
        //calculate number of dummy nodes
        node_t *n;
        edge_t *e;
        int nDummy = 0;

        for (n = agfstnode(g); n; n = agnxtnode(g, n))
            for (e = agfstout(g, n); e; e = agnxtout(g, e)) {
                if ((ND_rank(aghead(e)) > layerWidthInfo[nLayers].layerNumber
                     && ND_rank(agtail(e)) <
                     layerWidthInfo[nLayers].layerNumber)
                    || (ND_rank(aghead(e)) <
                        layerWidthInfo[nLayers].layerNumber
                        && ND_rank(agtail(e)) >
                        layerWidthInfo[nLayers].layerNumber)
                    )
                    nDummy++;
            }

        layerWidthInfo[nLayers].nDummyNodes = nDummy;
        layerWidthInfo[nLayers].width +=
            (layerWidthInfo[nLayers].nDummyNodes - 1) * GD_nodesep(g);
        nLayers++;
    }

    else {
        //undo increment of ranks and layerNumbers.*****************
        for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
            if (ND_rank(v) > layerWidthInfo[maxLayerIndex].layerNumber + 1)
                ND_rank(v)--;
        }

        for (i = 0; i < nLayers; i++) {
            if (layerWidthInfo[i].layerNumber >
                layerWidthInfo[maxLayerIndex].layerNumber + 1)
                layerWidthInfo[i].layerNumber--;
        }
    }
}
#endif

/* reduceMaxWidth2:
 * This is the main heuristic for partitioning the widest layer.
 * Partitioning is based on outdegrees of nodes.
 * Replace compFunction2 by compFunction3 if you want to partition
 * by node widths and heights.
 * FFDH procedure
 */
static void reduceMaxWidth2(graph_t * g)
{
    int i;
    int maxLayerIndex;
    double nextMaxWidth;
    double w = 0;
    double targetWidth;
    int fst;
    nodeGroup_t *fstNdGrp;
    int ndem;
    int p, q;
    int limit;
    int rem;
    int rem2;


    /* Find the widest layer. it must have at least 2 nodes. */
    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[sortedLayerIndex[i]].nNodeGroupsInLayer <= 1)
            continue;
        else {
            maxLayerIndex = sortedLayerIndex[i];
            /* get the width of the next widest layer */
            nextMaxWidth =
                (nLayers >
                 i + 1) ? layerWidthInfo[sortedLayerIndex[i +
                                                          1]].width : 0;
            break;
        }
    }

    if (i == nLayers)
        return;                 /* reduction of layerwidth is not possible. */

    /* sort the node groups in maxLayerIndex layer by height and 
     * then width, nonincreasing 
     */
    qsort(layerWidthInfo[maxLayerIndex].nodeGroupsInLayer,
          layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer,
          sizeof(nodeGroup_t *), compFunction2);

#if 0
    printf("\nSorted nodes in mx layer:\n---------------------------\n");
    for (i = 0; i < layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer; i++) {
        Agnode_t *node = layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i]->nodes[0];
        printf("%s. width=%lf, height=%lf\n",
               agnameof(node), node->width, node->height);
    }
#endif

    if (nextMaxWidth <= layerWidthInfo[maxLayerIndex].width / 4
        || nextMaxWidth >= layerWidthInfo[maxLayerIndex].width * 3 / 4)
        nextMaxWidth = layerWidthInfo[maxLayerIndex].width / 2;

    targetWidth = nextMaxWidth; /* layerWidthInfo[maxLayerIndex].width/2; */

    /* now partition the current layer into two or more 
     * layers (determined by the ranking algorithm)
     */
    fst = 0;
    ndem = 0;
    limit = layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer;
    rem = 0;
    rem2 = 0;

    /* initialize w, the width of the widest layer after partitioning */
    w = 0;

    for (i = 0; i < limit + rem; i++) {
        if (layerWidthInfo[maxLayerIndex].removed[i]) {
            rem++;
            continue;
        }

        if ((w +
             layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i]->width *
             DPI + (w > 0) * GD_nodesep(g) <= targetWidth)
            || !fst) {
            w += (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->
                width * DPI + (w > 0) * GD_nodesep(g);
            if (!fst) {
                fstNdGrp =
                    layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i];
                fst = 1;
            }
        } else {
            nodeGroup_t *ng =
                layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i];


#ifdef UNUSED
            /* The following code corrects w by adding dummy node spacing. 
             * It's no longer used
             */
            int l;
            for (l = 0; l < ng->nNodes; l++) {
                w += (ND_in(ng->nodes[l]).size - 1) * GD_nodesep(g);
            }
#endif

            for (p = 0; p < fstNdGrp->nNodes; p++)
                for (q = 0; q < ng->nNodes; q++) {
                    //printf("Trying to add virtual edge: %s -> %s\n",
                    //    agnameof(fstNdGrp->nodes[p]), agnameof(ng->nodes[q]));

                    /* The following code is for deletion of long virtual edges.
                     * It's no longer used.
                     */
#ifdef UNUSED
                    for (s = ND_in(ng->nodes[q]).size - 1; s >= 0; s--) {
                        ev = ND_in(ng->nodes[q]).list[s];

                        edge_t *et;
                        int fail = 0;
                        cnt = 0;

                        for (et = agfstin(g, aghead(ev)); et;
                             et = agnxtin(g, et)) {
                            if (aghead(et) == aghead(ev)
                                && agtail(et) == agtail(ev)) {
                                fail = 1;
                                break;
                            }
                        }

                        if (fail) {
                            //printf("FAIL DETECTED\n");
                            continue;
                        }


                        if (ED_edge_type(ev) == VIRTUAL
                            && ND_rank(aghead(ev)) > ND_rank(agtail(ev)) + 1) {
                            //printf("%d. inNode= %s.deleted: %s->%s\n",
                            //   test++, agnameof(ng->nodes[q]),
                            //   agnameof(agtail(ev)), agnameof(aghead(ev)));

                            delete_fast_edge(ev);
                            free(ev);
                        }
                    }
#endif

                    /* add a new virtual edge */
                    edge_t *newVEdge =
                        virtual_edge(fstNdGrp->nodes[p], ng->nodes[q],
                                     NULL);
                    ED_edge_type(newVEdge) = VIRTUAL;
                    ndem++;     /* increase number of node demotions */
                }

            /* the following code updates the layer width information. The 
             * update is not useful in the current version of the heuristic.
             */
            layerWidthInfo[maxLayerIndex].removed[i] = 1;
            rem2++;
            layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer--;
            /* SHOULD BE INCREASED BY THE SUM OF INDEG OF ALL NODES IN GROUP */
            layerWidthInfo[maxLayerIndex].nDummyNodes++;
            layerWidthInfo[maxLayerIndex].width -=
                (ng->width * DPI + GD_nodesep(g));
        }
    }
}

#ifdef UNUSED
/* balanceLayers:
 * The following is the layer balancing heuristic.
 * Balance the widths of the layers as much as possible.
 * It's no longer used.
 */
static void balanceLayers(graph_t * g)
{
    int maxLayerIndex, nextLayerIndex, i;
    double maxWidth, w;

    //get the max width layer number

    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[sortedLayerIndex[i]].nNodeGroupsInLayer <= 1
            ||
            layerWidthInfo[sortedLayerIndex[i]].layerNumber + 1 == nLayers)
            continue;
        else {
            maxLayerIndex = sortedLayerIndex[i];
            maxWidth = layerWidthInfo[maxLayerIndex].width;
            printf("Balancing: maxLayerIndex = %d\n", maxLayerIndex);
            break;
        }
    }

    if (i == nLayers)
        return;                 //reduction of layerwidth is not possible.

    //balancing ~~ packing by node demotion
    nextLayerIndex = -1;
    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[i].layerNumber ==
            layerWidthInfo[maxLayerIndex].layerNumber + 1) {
            nextLayerIndex = i;
        }
    }

    if (nextLayerIndex > -1) {
        //if (layerWidthInfo[nextLayerIndex].width <= 0.5*layerWidthInfo[maxLayerIndex].width)
        //{
        int changed = 0;
        w = 0;

        //demote nodes to the next layer
        for (i = 0; i < layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer;
             i++) {
            if (layerWidthInfo[maxLayerIndex].removed[i])
                continue;

            if (!checkHorizontalEdge
                (g, layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i],
                 nextLayerIndex)
                && layerWidthInfo[nextLayerIndex].width
                /*+ (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->width */
                <= layerWidthInfo[maxLayerIndex].width
                /*- (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->width*/
                ) {
                w += (layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i])->
                    width;
                changed++;

                int j;
                nodeGroup_t *ng =
                    layerWidthInfo[maxLayerIndex].nodeGroupsInLayer[i];

                layerWidthInfo[maxLayerIndex].removed[i] = 1;
                layerWidthInfo[maxLayerIndex].nNodeGroupsInLayer--;
                layerWidthInfo[maxLayerIndex].width -= (ng->width);
                layerWidthInfo[maxLayerIndex].nDummyNodes++;
                for (j = 0; j < ng->nNodes; j++)
                    ND_rank(ng->nodes[j])++;


                layerWidthInfo[nextLayerIndex].
                    nodeGroupsInLayer[layerWidthInfo[nextLayerIndex].
                                      nNodeGroupsInLayer] = ng;
                layerWidthInfo[nextLayerIndex].
                    removed[layerWidthInfo[nextLayerIndex].
                            nNodeGroupsInLayer] = 0;
                layerWidthInfo[nextLayerIndex].nNodeGroupsInLayer++;
                layerWidthInfo[nextLayerIndex].width +=
                    (ng->width + GD_nodesep(g));
            }

        }

        if (changed) {
            //printf("Demoted %d nodes\n", changed);
            return;
        }
        //}
    }
}

/* applyPacking:
 * The following is the initial packing heuristic
 * It's no longer used.
 */
static void applyPacking(graph_t * g, double targetAR)
{
    int i;

    sortedLayerIndex = N_NEW(agnnodes(g), int);

    for (i = 0; i < agnnodes(g); i++) {
        sortedLayerIndex[i] = i;
    }


    node_t *v;

    for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
        //printf("%s, rank = %d, ranktype = %d\n", agnameof(v), ND_rank(v), ND_ranktype(v));
    }

    //GD_nodesep(g) = 0.25;
    //GD_ranksep(g) = 0.25;
    //printf("Nodesep = %d, Ranksep = %d\n",GD_nodesep(g), GD_ranksep(g));


    for (i = 0; i < 1; i++) {
        //printf("iteration = %d\n----------------------\n", i);
        for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
            //printf("%s rank = %d\n", agnameof(v), ND_rank(v));
        }

        computeLayerWidths(g);
        sortLayers(g);
        reduceMaxWidth(g);

        //printf("====================\n");
    }


    int k;

    for (k = 0; k < nLayers - 1; k++) {
        int cnt = 0, tg;
        if (layerWidthInfo[k].nNodeGroupsInLayer > 7) {

            cnt = 0;
            tg = layerWidthInfo[k].nNodeGroupsInLayer - 7;

            for (i = layerWidthInfo[k].nNodeGroupsInLayer - 1; i >= 0; i--) {

                if (layerWidthInfo[k].removed[i])
                    continue;

                int j;
                nodeGroup_t *ng = layerWidthInfo[k].nodeGroupsInLayer[i];


                layerWidthInfo[k].removed[i] = 1;
                layerWidthInfo[k].nNodeGroupsInLayer--;
                layerWidthInfo[k].nDummyNodes++;
                layerWidthInfo[k].width -=
                    (ng->width * DPI + GD_nodesep(g));
                for (j = 0; j < ng->nNodes; j++)
                    ND_rank(ng->nodes[j])++;

                //create new layer
                layerWidthInfo[k +
                               1].nodeGroupsInLayer[layerWidthInfo[k +
                                                                   1].
                                                    nNodeGroupsInLayer] =
                    ng;
                layerWidthInfo[k + 1].nNodeGroupsInLayer++;
                //layerWidthInfo[k+1].layerNumber = ND_rank(ng->nodes[0]);

                //layerWidthInfo[k+1].width += ( ng->width*DPI + (layerWidthInfo[nLayers].nNodeGroupsInLayer > 1) * GD_nodesep(g) ); // just add the node widths now. 

                cnt++;

                if (cnt == tg)
                    break;

            }
        }
    }

    //calcualte the max width
    int maxW = 0;
    int nNodeG = 0, l, nDummy = 0;
    int index;

    for (k = 0; k < nLayers; k++) {
        //printf("Layer#=%d, #dumNd=%d, width=%0.1lf, node=%s\n", layerWidthInfo[k].layerNumber, layerWidthInfo[k].nDummyNodes, layerWidthInfo[k].width,
        // agnameof(layerWidthInfo[k].nodeGroupsInLayer[0]->nodes[0]));
        if (layerWidthInfo[k].width > maxW)     // && layerWidthInfo[k].nNodeGroupsInLayer > 0)
        {
            maxW = layerWidthInfo[k].width;
            nNodeG = layerWidthInfo[k].nNodeGroupsInLayer;
            l = layerWidthInfo[k].layerNumber;
            nDummy = layerWidthInfo[k].nDummyNodes;
            index = k;
        }
    }
    //printf("Ht=%d, MxW=%d, #ndGr=%d, #dumNd=%d, lyr#=%d, 1stNd=%s\n", (nLayers-1)*DPI, maxW, nNodeG, nDummy, l, agnameof(layerWidthInfo[index].nodeGroupsInLayer[0]->nodes[0]));

    // printf("Finally...\n------------------\n");
    for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
        //printf("%s, rank = %d, ranktype = %d\n", agnameof(v, ND_rank(v), ND_ranktype(v));
    }

}
#endif

/* applyPacking2:
 * The following is the packing heuristic for wide layout.
 */
static void applyPacking2(graph_t * g)
{
    int i;

    sortedLayerIndex = N_NEW(agnnodes(g), int);

    for (i = 0; i < agnnodes(g); i++) {
        sortedLayerIndex[i] = i;
    }

    computeLayerWidths(g);
    sortLayers(g);
    reduceMaxWidth2(g);

}

#ifdef UNUSED
/* applyPacking4:
 * The following is the packing heuristic for wide layout.
 * It's used with Nikolov-Healy healy heuristic.
 */
void applyPacking4(graph_t * g)
{
    int i;

    sortedLayerIndex = N_NEW(agnnodes(g), int);

    for (i = 0; i < agnnodes(g); i++) {
        sortedLayerIndex[i] = i;
    }


    for (i = 0; i < 1; i++) {
        /*    printf("iteration = %d\n----------------------\n", i);
           for (v = agfstnode(g); v; v = agnxtnode(g,v))
           {
           printf("%s rank = %d\n", agnameof(v), ND_rank(v));
           }
         */


        computeLayerWidths(g);
        sortLayers(g);
        reduceMaxWidth2(g);
        //printf("====================\n");
    }
}

/*
 *       NOCOLOV & HEALY'S NODE PROMOTION HEURISTIC
 */

/****************************************************************
 * This data structure is needed for backing up node information
 * during node promotion
 ****************************************************************/
typedef struct myNodeInfo_t {
    int indegree;
    int outdegree;
    int rank;
    Agnode_t *node;
} myNodeInfo_t;

myNodeInfo_t *myNodeInfo;


/* getMaxLevelNumber:
 * return the maximum level number assigned
 */
int getMaxLevelNumber(graph_t * g)
{
    int max;
    Agnode_t *n;

    max = ND_rank(agfstnode(g));

    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        if (ND_rank(n) > max)
            max = ND_rank(n);
    }

    return max;
}

/* countDummyDiff:
 * return the difference in the count of dummy nodes before 
 * and after promoting the node v
 */
static int countDummyDiff(graph_t * g, Agnode_t * v, int max)
{
    int dummydiff = 0;
    Agedge_t *e;
    Agnode_t *u;
    int maxR = 0;
    int j;

    for (j = 0; j < ND_in(v).size; j++) {
        e = ND_in(v).list[j];
        u = agtail(e);

        if (myNodeInfo[ND_id(u)].rank == myNodeInfo[ND_id(v)].rank + 1) {
            dummydiff += countDummyDiff(g, u, max);
        }
    }

    if (myNodeInfo[ND_id(v)].rank + 1 < max
        || (ND_in(v).size == 0 && myNodeInfo[ND_id(v)].rank + 1 <= max))
        myNodeInfo[ND_id(v)].rank += 1;

    dummydiff = dummydiff - ND_in(v).size + ND_out(v).size;


    return dummydiff;
}

/* applyPromotionHeuristic:
 * Node Promotion Heuristic
 * by Nikolov and Healy
 */
static void applyPromotionHeuristic(graph_t * g)
{
    graph_t graphBkup = *g;
    Agnode_t *v;
    int promotions;

    int max = getMaxLevelNumber(g);
    int count = 0;
    int nNodes = agnnodes(g);
    int i, j;

    myNodeInfo = N_NEW(nNodes, myNodeInfo_t);
    myNodeInfo_t *myNodeInfoBak = N_NEW(nNodes, myNodeInfo_t);

    for (v = agfstnode(g), i = 0; v; v = agnxtnode(g, v), i++) {
        myNodeInfo[i].indegree = ND_in(v).size;
        myNodeInfo[i].outdegree = ND_out(v).size;
        myNodeInfo[i].rank = ND_rank(v);
        myNodeInfo[i].node = v;
        ND_id(v) = i;

        myNodeInfoBak[i] = myNodeInfo[i];
    }

    do {
        promotions = 0;

        for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
            if (ND_in(v).size > 0) {
                if (countDummyDiff(g, v, max) <= 0) {
                    promotions++;

                    for (j = 0; j < nNodes; j++) {
                        myNodeInfoBak[j] = myNodeInfo[j];
                    }

                } else {
                    for (j = 0; j < nNodes; j++) {
                        myNodeInfo[j] = myNodeInfoBak[j];
                    }
                }
            }
        }
        count++;
    } while (count < max);

    for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
        ND_rank(v) = myNodeInfo[ND_id(v)].rank;
    }
}

/*
 *       LONGEST PATH ALGORITHM
 */

/* allNeighborsAreBelow:
 * Return 1 if all the neighbors of n already ranked, else 0
 */
static int allNeighborsAreBelow(Agnode_t * n)
{
    Agedge_t *e;
    graph_t *g = agraphof(n);
    int i;

    //for (e = agfstout(g,n); e; e = agnxtout(g,e))
    for (i = 0; i < ND_out(n).size; i++) {
        e = ND_out(n).list[i];
        if (ED_edge_type(e) == VIRTUAL) {
            if (ED_to_orig(e) != NULL)
                e = ED_to_orig(e);
            else if (ND_node_type(aghead(e)) == VIRTUAL)
                continue;
        }

        if (ND_pinned(aghead(e)) != 2)  //neighbor of n is not below
        {
            return 0;
        }
    }

    return 1;
}

/* reverseLevelNumbers:
 * In Nikolov and Healy ranking, bottom layer ranking is  0 and
 * top layer ranking is the maximum. 
 * Graphviz does the opposite.
 * This function does the reversing from Nikolov to Graphviz.
 */
static void reverseLevelNumbers(graph_t * g)
{
    Agnode_t *n;
    int max;

    max = getMaxLevelNumber(g);

    //printf("max = %d\n", max);

    //return;
    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        ND_rank(n) = max - ND_rank(n);
    }
}

/* doSameRank:
 * Maintain the same ranking constraint.
 * Can only be used with the Nikolov and Healy algorithm
 */
static void doSameRank(graph_t * g)
{
    int i;
    for (i = 0; i < nNodeGroups; i++) {
        int j;

        for (j = 0; j < nodeGroups[i].nNodes; j++) {
            if (ND_ranktype(nodeGroups[i].nodes[j]) == SAMERANK)        //once we find a SAMERANK node in a group- make all the members of the group SAMERANK
            {
                int k;
                int r = ND_rank(UF_find(nodeGroups[i].nodes[j]));
                for (k = 0; k < nodeGroups[i].nNodes; k++) {
                    ND_rank(nodeGroups[i].
                            nodes[(j + k) % nodeGroups[i].nNodes]) = r;
                }

                break;
            }
        }
    }
}

/* doMinRank:
 * Maintain the MIN ranking constraint.
 * Can only be used with the Nikolov and Healy algorithm
 */
void doMinRank(graph_t * g)
{
    int i;
    for (i = 0; i < nNodeGroups; i++) {
        int j;

        for (j = 0; j < nodeGroups[i].nNodes; j++) {
            if (ND_ranktype(nodeGroups[i].nodes[j]) == MINRANK) //once we find a MINRANK node in a group- make the rank of all the members of the group 0
            {
                int k;
                for (k = 0; k < nodeGroups[i].nNodes; k++) {
                    ND_rank(nodeGroups[i].
                            nodes[(j + k) % nodeGroups[i].nNodes]) = 0;
                    if (ND_ranktype
                        (nodeGroups[i].
                         nodes[(j + k) % nodeGroups[i].nNodes]) !=
                        SOURCERANK)
                        ND_ranktype(nodeGroups[i].
                                    nodes[(j +
                                           k) % nodeGroups[i].nNodes]) =
                            MINRANK;
                }

                break;
            }
        }
    }
}

/* getMaxRank:
 * Return the maximum rank among all nodes.
 */
static int getMaxRank(graph_t * g)
{
    int i;
    node_t *v;
    int maxR = ND_rank(agfstnode(g));
    for (v = agfstnode(g); v; v = agnxtnode(g, v)) {
        if (ND_rank(v) > maxR)
            maxR = ND_rank(v);
    }

    return maxR;
}

/* doMaxRank:
 * Maintain the MAX ranking constraint.
 * Can only be used with the Nikolov and Healy algorithm
 */
static void doMaxRank(graph_t * g)
{
    int i;
    for (i = 0; i < nNodeGroups; i++) {
        int j;
        int maxR = getMaxRank(g);

        for (j = 0; j < nodeGroups[i].nNodes; j++) {
            if (ND_ranktype(nodeGroups[i].nodes[j]) == MAXRANK) //once we find a MAXRANK node in a group- make the rank of all the members of the group MAX
            {
                int k;
                for (k = 0; k < nodeGroups[i].nNodes; k++) {
                    ND_rank(nodeGroups[i].
                            nodes[(j + k) % nodeGroups[i].nNodes]) = maxR;
                    if (ND_ranktype
                        (nodeGroups[i].
                         nodes[(j + k) % nodeGroups[i].nNodes]) !=
                        SINKRANK)
                        ND_ranktype(nodeGroups[i].
                                    nodes[(j +
                                           k) % nodeGroups[i].nNodes]) =
                            MAXRANK;
                }

                break;
            }
        }
    }
}

/* doSourceRank:
 * Maintain the SOURCE ranking constraint.
 * Can only be used with the Nikolov and Healy algorithm
 */
static void doSourceRank(graph_t * g)
{
    int i;
    int flag = 0;

    for (i = 0; i < nNodeGroups; i++) {
        int j;

        for (j = 0; j < nodeGroups[i].nNodes; j++) {
            //once we find a SOURCERANK node in a group- make the rank of all the members of the group 0
            if (ND_ranktype(nodeGroups[i].nodes[j]) == SOURCERANK) {
                int k;
                for (k = 0; k < nodeGroups[i].nNodes; k++) {
                    ND_rank(nodeGroups[i].
                            nodes[(j + k) % nodeGroups[i].nNodes]) = 0;
                    ND_ranktype(nodeGroups[i].
                                nodes[(j + k) % nodeGroups[i].nNodes]) =
                        SOURCERANK;
                }

                flag = 1;
                break;
            }
        }
    }

    if (!flag)
        return;

    flag = 0;

    //The SourceRank group might be the only group having rank 0. Check if increment of ranking of other nodes is necessary at all.
    for (i = 0; i < nNodeGroups; i++) {
        if (nodeGroups[i].nNodes > 0
            && ND_ranktype(nodeGroups[i].nodes[0]) != SOURCERANK
            && ND_rank(nodeGroups[i].nodes[0]) == 0) {
            flag = 1;
            break;
        }
    }


    if (!flag)
        return;

    //Now make all NON-SourceRank nodes' ranking nonzero (increment)
    for (i = 0; i < nNodeGroups; i++) {
        if (nodeGroups[i].nNodes > 0
            && ND_ranktype(nodeGroups[i].nodes[0]) != SOURCERANK) {
            int j;

            for (j = 0; j < nodeGroups[i].nNodes; j++) {
                ND_rank(nodeGroups[i].nodes[j])++;
            }
        }
    }
}

/* doSinkRank:
 * Maintain the SINK ranking constraint.
 * Can only be used with the Nikolov and Healy algorithm
 */
static void doSinkRank(graph_t * g)
{
    int i, max;
    int flag = 0;

    max = getMaxRank(g);


    //Check if any non-sink node has rank = max
    for (i = 0; i < nNodeGroups; i++) {
        if (nodeGroups[i].nNodes > 0
            && ND_ranktype(nodeGroups[i].nodes[0]) != SINKRANK
            && ND_rank(nodeGroups[i].nodes[0]) == max) {
            flag = 1;
            break;
        }
    }

    if (!flag)
        return;

    for (i = 0; i < nNodeGroups; i++) {
        int j;

        for (j = 0; j < nodeGroups[i].nNodes; j++) {
            if (ND_ranktype(nodeGroups[i].nodes[j]) == SINKRANK)        //once we find a SINKRANK node in a group- make the rank of all the members of the group: max+1
            {
                int k;
                for (k = 0; k < nodeGroups[i].nNodes; k++) {
                    ND_rank(nodeGroups[i].
                            nodes[(j + k) % nodeGroups[i].nNodes]) =
                        max + 1;
                    ND_ranktype(nodeGroups[i].
                                nodes[(j + k) % nodeGroups[i].nNodes]) =
                        SINKRANK;
                }

                break;
            }
        }
    }
}

/* rank2: 
 * Initial codes for ranking (Nikolov-Healy).
 * It's no longer used.
 */
void rank2(graph_t * g)
{
    int currentLayer = 1;
    int nNodes = agnnodes(g);
    int nEdges = agnedges(g);
    int nPinnedNodes = 0, nSelected = 0;
    Agnode_t *n, **UArray;
    int USize = 0;
    int i, prevSize = 0;

    UArray = N_NEW(nEdges * 2, Agnode_t *);

    /* make all pinning values 0 */
    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        ND_pinned(n) = 0;
    }

    while (nPinnedNodes != nNodes) {
        for (nSelected = 0, n = agfstnode(g); n; n = agnxtnode(g, n)) {
            if (ND_pinned(n) == 0) {
                if (allNeighborsAreBelow(n)) {
                    ND_pinned(n) = 1;

                    UArray[USize] = n;
                    USize++;

                    ND_rank(n) = currentLayer;
                    nPinnedNodes++;
                    nSelected++;
                }
            }
        }

        if (nSelected == 0)     //no node has been selected
        {
            currentLayer++;
            for (i = prevSize; i < USize; i++) {
                ND_pinned(UArray[i]) = 2;       //pinning value of 2 indicates this node is below the current node under consideration
            }

            prevSize = USize;
        }
    }

    //Apply Nikolov's node promotion heuristic
    applyPromotionHeuristic(g);

    //this is for the sake of graphViz layer numbering scheme
    reverseLevelNumbers(g);

    computeNodeGroups(g);       //groups of UF DS nodes

    //modify the ranking to respect the same ranking constraint
    doSameRank(g);

    //satisfy min ranking constraints
    doMinRank(g);
    doMaxRank(g);

    //satisfy source ranking constraints
    doSourceRank(g);
    doSinkRank(g);

    //Apply the FFDH algorithm to achieve better aspect ratio;
    applyPacking(g, 1);         //achieve an aspect ratio of 1
}
#endif

/****************************************************************
 * Initialize all the edge types to NORMAL 
 ****************************************************************/
void initEdgeTypes(graph_t * g)
{
    edge_t *e;
    node_t *n;
    int lc;

    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        for (lc = 0; lc < ND_in(n).size; lc++) {
            e = ND_in(n).list[lc];
            ED_edge_type(e) = NORMAL;
        }
    }
}

/* computeCombiAR:
 * Compute and return combinatorial aspect ratio 
 * =
 * Width of the widest layer / Height 
 * (in ranking phase)
 */
static double computeCombiAR(graph_t * g)
{
    int i, maxLayerIndex;
    double maxW = 0;
    double maxH;
    double ratio;

    computeLayerWidths(g);
    maxH = (nLayers - 1) * GD_ranksep(g);

    for (i = 0; i < nLayers; i++) {
        if (maxW <
            layerWidthInfo[i].width +
            layerWidthInfo[i].nDummyNodes * GD_nodesep(g)) {
            maxW =
                layerWidthInfo[i].width +
                layerWidthInfo[i].nDummyNodes * GD_nodesep(g);
            maxLayerIndex = i;
        }
        maxH += layerWidthInfo[i].height;
    }

    ratio = maxW / maxH;

    return ratio;
}

#ifdef UNUSED
/* applyExpansion:
 * Heuristic for expanding very narrow graphs by edge reversal.
 * Needs improvement.
 */
void applyExpansion(graph_t * g)
{
    node_t *sink = NULL;
    int i, k;
    edge_t *e;

    computeLayerWidths(g);

    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[i].layerNumber == nLayers / 2) {
            k = i;
            break;
        }
    }

    //now reverse the edges, from the k-th layer nodes to their parents
    for (i = 0; i < layerWidthInfo[k].nNodeGroupsInLayer; i++) {
        int p;
        nodeGroup_t *ng = layerWidthInfo[k].nodeGroupsInLayer[i];
        for (p = 0; p < ng->nNodes; p++) {
            node_t *nd = ng->nodes[p];

            while (e = ND_in(nd).list[0]) {
                printf("Reversing edge: %s->%s\n", agnemeof(agtail(e)),
                       agnameof(aghead(e)));
                reverse_edge(e);
            }

            int j, l;
            node_t *v3;
            edge_t *e3;
            for (v3 = agfstnode(g); v3; v3 = agnxtnode(g, v3)) {
                for (e3 = agfstout(g, v3); e3; e3 = agnxtout(g, e3)) {
                    if (ND_rank(aghead(e3)) > k && ND_rank(agtail(e3)) < k) {
                        printf("Reversing long edge: %s->%s\n",
                               agnameof(agtail(e3)), agnameof(aghead(e3)));
                        reverse_edge(e3);
                    }

                }
            }

            /*for (l = 0; l < nLayers; l++) {
                if (layerWidthInfo[l].layerNumber <= k)
                    continue;

                for (j = 0; j < layerWidthInfo[l].nNodeGroupsInLayer; j++) {
                    int q;
                    nodeGroup_t *ng2 = layerWidthInfo[l].nodeGroupsInLayer[j];
                    for (q = 0; q < ng2->nNodes; q++) {
                        node_t *nd2 = ng2->nodes[q];
                        edge_t *e2;
                        int s = 0;
                        while (e2 = ND_in(nd2).list[s]) {
                            if (ND_rank(agtail(e2)) < k) {
                                printf("Reversing edge: %s->%s\n",
                                    agnameof(agtail(e2)), agnameof(aghead(e2)));
                                getchar();
                                //reverse_edge(e2);
                            }
                            else s++;
                        }
                    }
                }
            } */

            if (sink == NULL) {
                int brFlag = 1;
                for (l = 0; l < nLayers && brFlag; l++) {
                    for (j = 0;
                         j < layerWidthInfo[l].nNodeGroupsInLayer
                         && brFlag; j++) {
                        int q;
                        nodeGroup_t *ng2 =
                            layerWidthInfo[l].nodeGroupsInLayer[j];
                        for (q = 0; q < ng2->nNodes && brFlag; q++) {
                            node_t *nd2 = ng2->nodes[q];
                            if (ND_in(nd2).size == 0) {
                                sink = nd2;
                                brFlag = 0;
                            }
                        }
                    }
                }

            }

            virtual_edge(nd,    /*sink */
                         layerWidthInfo[0].nodeGroupsInLayer[0]->nodes[0],
                         NULL);
        }
    }

    //collapse_sets(g);
}
#endif

/* zapLayers:
 * After applying the expansion heuristic, some layers are
 * found to be empty.
 * This function removes the empty layers.
 */
static void zapLayers(graph_t * g)
{
    int i, j;
    int start = 0;
    int count = 0;

    /* the layers are sorted by the layer number.  now zap the empty layers */

    for (i = 0; i < nLayers; i++) {
        if (layerWidthInfo[i].nNodeGroupsInLayer == 0) {
            if (count == 0)
                start = layerWidthInfo[i].layerNumber;
            count++;
        } else if (count && layerWidthInfo[i].layerNumber > start) {
            for (j = 0; j < layerWidthInfo[i].nNodeGroupsInLayer; j++) {
                int q;
                nodeGroup_t *ng = layerWidthInfo[i].nodeGroupsInLayer[j];
                for (q = 0; q < ng->nNodes; q++) {
                    node_t *nd = ng->nodes[q];
                    ND_rank(nd) -= count;
                }
            }
        }
    }
}

/* rank3: 
 * ranking function for dealing with wide/narrow graphs,
 * or graphs with varying node widths and heights.
 * This function iteratively calls dot's rank1() function and 
 * applies packing (by calling the applyPacking2 function. 
 * applyPacking2 function calls the reduceMaxWidth2 function
 * for partitioning the widest layer).
 * Initially the iterations argument is -1, for which rank3
 * callse applyPacking2 function until the combinatorial aspect
 * ratio is <= the desired aspect ratio.
 */
void rank3(graph_t * g, aspect_t * asp)
{
    Agnode_t *n;
    int i;
    int iterations = asp->nextIter;

    computeNodeGroups(g);       /* groups of UF DS nodes */

    for (i = 0; i < iterations || iterations == -1; i++) {
        /* initialize all ranks to be 0 */
        for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
            ND_rank(n) = 0;
        }

        /* need to compute ranking first--- by Network flow */

        rank1(g);

        asp->combiAR = computeCombiAR(g);
        if (Verbose)
            fprintf(stderr, "combiAR = %lf\n", asp->combiAR);


        /* Uncomment the following codes, for working with narrow graphs */
#ifdef UNUSED
        if (combiAR < 0.8 * targetAR) {
            char str[20];
            printf("Apply expansion? (y/n):");
            scanf("%s", str);
            if (strcmp(str, "y") == 0)
                applyExpansion(g);
            break;
        } else
#endif
        if (iterations == -1 && asp->combiAR <= asp->targetAR) {
            asp->prevIterations = asp->curIterations;
            asp->curIterations = i;

            break;
        }
        /* Apply the FFDH algorithm to reduce the aspect ratio; */
        applyPacking2(g);
    }

    /* do network flow once again... incorporating the added edges */
    rank1(g);

    computeLayerWidths(g);
    zapLayers(g);
    asp->combiAR = computeCombiAR(g);
}

#ifdef UNUSED
/* NikolovHealy:
 * Nikolov-Healy approach to ranking.
 * First, use longest path algorithm.
 * Then use node promotion heuristic.
 * This function is called by rank4 function.
 */
static void NikolovHealy(graph_t * g)
{
    int currentLayer = 1;
    int nNodes = agnnodes(g);
    int nEdges = agnedges(g);
    int nPinnedNodes = 0, nSelected = 0;
    Agnode_t *n, **UArray;
    int USize = 0;
    int i, prevSize = 0;

    /************************************************************************
     * longest path algorithm
     ************************************************************************/
    UArray = N_NEW(nEdges * 2, Agnode_t *);

    /* make all pinning values 0 */
    for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
        ND_pinned(n) = 0;
    }

    while (nPinnedNodes != nNodes) {
        for (nSelected = 0, n = agfstnode(g); n; n = agnxtnode(g, n)) {
            if (ND_pinned(n) == 0) {
                if (allNeighborsAreBelow(n)) {
                    ND_pinned(n) = 1;

                    UArray[USize] = n;
                    USize++;

                    ND_rank(n) = currentLayer;
                    nPinnedNodes++;
                    nSelected++;
                }
            }
        }

        if (nSelected == 0)     //no node has been selected
        {
            currentLayer++;
            for (i = prevSize; i < USize; i++) {
                ND_pinned(UArray[i]) = 2;       //pinning value of 2 indicates this node is below the current node under consideration
            }

            prevSize = USize;
        }

    }

    /************************************************************************
     * end of longest path algorithm
     ************************************************************************/

    //Apply node promotion heuristic
    applyPromotionHeuristic(g);

    //this is for the sake of graphViz layer numbering scheme
    reverseLevelNumbers(g);

}


/* rank4:
 * This function is calls the NikolovHealy function
 * for ranking in the Nikolov-Healy approach.
 */
void rank4(graph_t * g, int iterations)
{
    int currentLayer = 1;
    int nNodes = agnnodes(g);
    int nEdges = agnedges(g);
    int nPinnedNodes = 0, nSelected = 0;
    Agnode_t *n, **UArray;
    int USize = 0;
    int i, prevSize = 0;

    int it;
    printf("# of interations of packing: ");
    scanf("%d", &it);
    printf("it=%d\n", it);

    computeNodeGroups(g);       //groups of UF DS nodes

    for (i = 0; i < it; i++) {
        for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
            ND_rank(n) = 0;
        }

        NikolovHealy(g);

        edge_t *e;
        int cnt = 0;
        int lc;


        combiAR = computeCombiAR(g);
        printf("%d. combiAR = %lf\n", i, combiAR);

        /*
           //modify the ranking to respect the same ranking constraint
           doSameRank(g);

           //satisfy min ranking constraints
           doMinRank(g);
           doMaxRank(g);

           //satisfy source ranking constraints
           doSourceRank(g);
           doSinkRank(g);
         */

        //Apply the FFDH algorithm to achieve better aspect ratio;
        applyPacking4(g);

    }

}
#endif

/* init_UF_size:
 * Initialize the Union Find data structure
 */
void init_UF_size(graph_t * g)
{
    node_t *n;

    for (n = agfstnode(g); n; n = agnxtnode(g, n))
        ND_UF_size(n) = 0;
}