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/* ========================================================================== */
/* === Source/Mongoose_Coarsening.cpp ======================================= */
/* ========================================================================== */
/* -----------------------------------------------------------------------------
* Mongoose Graph Partitioning Library Copyright (C) 2017-2018,
* Scott P. Kolodziej, Nuri S. Yeralan, Timothy A. Davis, William W. Hager
* Mongoose is licensed under Version 3 of the GNU General Public License.
* Mongoose is also available under other licenses; contact authors for details.
* -------------------------------------------------------------------------- */
/**
* Coarsening of a graph given a previously determined matching
*
* In order to operate on extremely large graphs, a pre-processing is
* done to reduce the size of the graph while maintaining its overall structure.
* Given a matching of vertices with other vertices (e.g. heavy edge matching,
* random, etc.), coarsening constructs the new, coarsened graph.
*/
#include "Mongoose_Coarsening.hpp"
#include "Mongoose_Debug.hpp"
#include "Mongoose_Internal.hpp"
#include "Mongoose_Logger.hpp"
namespace Mongoose
{
/**
* @brief Coarsen a Graph given a previously calculated matching
*
* Given a Graph @p G, coarsen returns a new Graph that is coarsened according
* to the matching given by G->matching, G->matchmap, and G->invmatchmap.
* G->matching must be built such that matching[a] = b+1 and matching[b] = a+1
* if vertices a and b are matched. G->matchmap is a mapping from fine to coarse
* vertices, so matchmap[a] = matchmap[b] = c if vertices a and b are matched
* and mapped to vertex c in the coarse graph. Likewise, G->invmatchmap is
* one possible inverse of G->matchmap, so invmatchmap[c] = a or
* invmatchmap[c] = b if a coarsened vertex c represents the matching of
* vertices a and b in the refined graph.
*
* @code
* Graph coarsened_graph = coarsen(large_graph, options);
* @endcode
*
* @param graph Graph to be coarsened
* @param options Option struct specifying if debug checks should be done
* @return A coarsened version of G
* @note Allocates memory for the coarsened graph, but frees on error.
*/
EdgeCutProblem *coarsen(EdgeCutProblem *graph, const EdgeCut_Options *options)
{
(void)options; // Unused variable
Logger::tic(CoarseningTiming);
Int cn = graph->cn;
Int *Gp = graph->p;
Int *Gi = graph->i;
double *Gx = graph->x;
double *Gw = graph->w;
Int *matchmap = graph->matchmap;
Int *invmatchmap = graph->invmatchmap;
/* Build the coarse graph */
EdgeCutProblem *coarseGraph = EdgeCutProblem::create(graph);
if (!coarseGraph)
return NULL;
Int *Cp = coarseGraph->p;
Int *Ci = coarseGraph->i;
double *Cx = coarseGraph->x;
double *Cw = coarseGraph->w;
double *gains = coarseGraph->vertexGains;
Int munch = 0;
double X = 0.0;
/* edge and vertex weights always appear in a coarse graph */
ASSERT(Cx != NULL);
ASSERT(Cw != NULL);
/* Hashtable stores column pointer values. */
Int *htable
= (Int *)SuiteSparse_malloc(static_cast<size_t>(cn), sizeof(Int));
if (!htable)
{
coarseGraph->~EdgeCutProblem();
return NULL;
}
for (Int i = 0; i < cn; i++)
htable[i] = -1;
/* For each vertex in the coarse graph. */
for (Int k = 0; k < cn; k++)
{
/* Load up the inverse matching */
Int v[3] = { -1, -1, -1 };
v[0] = invmatchmap[k];
v[1] = graph->getMatch(v[0]);
if (v[0] == v[1])
{
v[1] = -1;
}
else
{
v[2] = graph->getMatch(v[1]);
if (v[0] == v[2])
{
v[2] = -1;
}
}
Int ps = Cp[k] = munch; /* The munch start for this column */
double vertexWeight = 0.0;
double sumEdgeWeights = 0.0;
for (Int i = 0; i < 3 && v[i] != -1; i++)
{
/* Read the matched vertex and accumulate the vertex weight. */
Int vertex = v[i];
vertexWeight += (Gw) ? Gw[vertex] : 1;
for (Int p = Gp[vertex]; p < Gp[vertex + 1]; p++)
{
Int toCoarsened = matchmap[Gi[p]];
if (toCoarsened == k)
continue; /* Delete self-edges */
/* Read the edge weight and accumulate the sum of edge weights.
*/
double edgeWeight = (Gx) ? Gx[p] : 1;
sumEdgeWeights += (Gx) ? Gx[p] : 1;
/* Check the hashtable before scattering. */
Int cp = htable[toCoarsened];
if (cp < ps) /* Hasn't been seen yet this column */
{
htable[toCoarsened] = munch;
Ci[munch] = toCoarsened;
Cx[munch] = edgeWeight;
munch++;
}
/* If the entry already exists & we have edge weights,
* sum the edge weights here. */
else
{
Cx[cp] += edgeWeight;
}
}
}
/* Save the vertex weight. */
Cw[k] = vertexWeight;
/* Save the sum of edge weights and initialize the gain for k. */
X += sumEdgeWeights;
gains[k] = -sumEdgeWeights;
}
/* Set the last column pointer */
Cp[cn] = munch;
coarseGraph->nz = munch;
/* Save the sum of edge weights on the graph. */
coarseGraph->X = X;
coarseGraph->H = 2.0 * X;
coarseGraph->worstCaseRatio = graph->worstCaseRatio;
/* Cleanup resources */
SuiteSparse_free(htable);
#ifndef NDEBUG
/* If we want to do expensive checks, make sure we didn't break
* the problem into multiple connected components. */
double W = 0.0;
for (Int k = 0; k < cn; k++)
{
W += Cw[k];
}
ASSERT(W == coarseGraph->W);
#endif
Logger::toc(CoarseningTiming);
/* Return the coarse graph */
return coarseGraph;
}
} // end namespace Mongoose
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