/* glpnet09.c */

/***********************************************************************

*  This code is part of GLPK (GNU Linear Programming Kit).

*

*  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

*  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

*  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

*  E-mail: <mao@gnu.org>.

*

*  GLPK is free software: you can redistribute it and/or modify it

*  under the terms of the GNU General Public License as published by

*  the Free Software Foundation, either version 3 of the License, or

*  (at your option) any later version.

*

*  GLPK is distributed in the hope that it will be useful, but WITHOUT

*  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

*  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public

*  License for more details.

*

*  You should have received a copy of the GNU General Public License

*  along with GLPK. If not, see <http://www.gnu.org/licenses/>.

***********************************************************************/

#include "glpapi.h"

#include "glpnet.h"

/***********************************************************************

*  NAME

*

*  kellerman - cover edges by cliques with Kellerman's heuristic

*

*  SYNOPSIS

*

*  #include "glpnet.h"

*  int kellerman(int n, int (*func)(void *info, int i, int ind[]),

*     void *info, glp_graph *H);

*

*  DESCRIPTION

*

*  The routine kellerman implements Kellerman's heuristic algorithm

*  to find a minimal set of cliques which cover all edges of specified

*  graph G = (V, E).

*

*  The parameter n specifies the number of vertices |V|, n >= 0.

*

*  Formal routine func specifies the set of edges E in the following

*  way. Running the routine kellerman calls the routine func and passes

*  to it parameter i, which is the number of some vertex, 1 <= i <= n.

*  In response the routine func should store numbers of all vertices

*  adjacent to vertex i to locations ind[1], ind[2], ..., ind[len] and

*  return the value of len, which is the number of adjacent vertices,

*  0 <= len <= n. Self-loops are allowed, but ignored. Multiple edges

*  are not allowed.

*

*  The parameter info is a transit pointer (magic cookie) passed to the

*  formal routine func as its first parameter.

*

*  The result provided by the routine kellerman is the bipartite graph

*  H = (V union C, F), which defines the covering found. (The program

*  object of type glp_graph specified by the parameter H should be

*  previously created with the routine glp_create_graph. On entry the

*  routine kellerman erases the content of this object with the routine

*  glp_erase_graph.) Vertices of first part V correspond to vertices of

*  the graph G and have the same ordinal numbers 1, 2, ..., n. Vertices

*  of second part C correspond to cliques and have ordinal numbers

*  n+1, n+2, ..., n+k, where k is the total number of cliques in the

*  edge covering found. Every edge f in F in the program object H is

*  represented as arc f = (i->j), where i in V and j in C, which means

*  that vertex i of the graph G is in clique C[j], 1 <= j <= k. (Thus,

*  if two vertices of the graph G are in the same clique, these vertices

*  are adjacent in G, and corresponding edge is covered by that clique.)

*

*  RETURNS

*

*  The routine Kellerman returns k, the total number of cliques in the

*  edge covering found.

*

*  REFERENCE

*

*  For more details see: glpk/doc/notes/keller.pdf (in Russian). */

struct set

{     /* set of vertices */

      int size;

      /* size (cardinality) of the set, 0 <= card <= n */

      int *list; /* int list[1+n]; */

      /* the set contains vertices list[1,...,size] */

      int *pos; /* int pos[1+n]; */

      /* pos[i] > 0 means that vertex i is in the set and

         list[pos[i]] = i; pos[i] = 0 means that vertex i is not in

         the set */

};

int kellerman(int n, int (*func)(void *info, int i, int ind[]),

      void *info, void /* glp_graph */ *H_)

{     glp_graph *H = H_;

      struct set W_, *W = &W_, V_, *V = &V_;

      glp_arc *a;

      int i, j, k, m, t, len, card, best;

      xassert(n >= 0);

      /* H := (V, 0; 0), where V is the set of vertices of graph G */

      glp_erase_graph(H, H->v_size, H->a_size);

      glp_add_vertices(H, n);

      /* W := 0 */

      W->size = 0;

      W->list = xcalloc(1+n, sizeof(int));

      W->pos = xcalloc(1+n, sizeof(int));

      memset(&W->pos[1], 0, sizeof(int) * n);

      /* V := 0 */

      V->size = 0;

      V->list = xcalloc(1+n, sizeof(int));

      V->pos = xcalloc(1+n, sizeof(int));

      memset(&V->pos[1], 0, sizeof(int) * n);

      /* main loop */

      for (i = 1; i <= n; i++)

      {  /* W must be empty */

         xassert(W->size == 0);

         /* W := { j : i > j and (i,j) in E } */

         len = func(info, i, W->list);

         xassert(0 <= len && len <= n);

         for (t = 1; t <= len; t++)

         {  j = W->list[t];

            xassert(1 <= j && j <= n);

            if (j >= i) continue;

            xassert(W->pos[j] == 0);

            W->list[++W->size] = j, W->pos[j] = W->size;

         }

         /* on i-th iteration we need to cover edges (i,j) for all

            j in W */

         /* if W is empty, it is a special case */

         if (W->size == 0)

         {  /* set k := k + 1 and create new clique C[k] = { i } */

            k = glp_add_vertices(H, 1) - n;

            glp_add_arc(H, i, n + k);

            continue;

         }

         /* try to include vertex i into existing cliques */

         /* V must be empty */

         xassert(V->size == 0);

         /* k is the number of cliques found so far */

         k = H->nv - n;

         for (m = 1; m <= k; m++)

         {  /* do while V != W; since here V is within W, we can use

               equivalent condition: do while |V| < |W| */

            if (V->size == W->size) break;

            /* check if C[m] is within W */

            for (a = H->v[n + m]->in; a != NULL; a = a->h_next)

            {  j = a->tail->i;

               if (W->pos[j] == 0) break;

            }

            if (a != NULL) continue;

            /* C[m] is within W, expand clique C[m] with vertex i */

            /* C[m] := C[m] union {i} */

            glp_add_arc(H, i, n + m);

            /* V is a set of vertices whose incident edges are already

               covered by existing cliques */

            /* V := V union C[m] */

            for (a = H->v[n + m]->in; a != NULL; a = a->h_next)

            {  j = a->tail->i;

               if (V->pos[j] == 0)

                  V->list[++V->size] = j, V->pos[j] = V->size;

            }

         }

         /* remove from set W the vertices whose incident edges are

            already covered by existing cliques */

         /* W := W \ V, V := 0 */

         for (t = 1; t <= V->size; t++)

         {  j = V->list[t], V->pos[j] = 0;

            if (W->pos[j] != 0)

            {  /* remove vertex j from W */

               if (W->pos[j] != W->size)

               {  int jj = W->list[W->size];

                  W->list[W->pos[j]] = jj;

                  W->pos[jj] = W->pos[j];

               }

               W->size--, W->pos[j] = 0;

            }

         }

         V->size = 0;

         /* now set W contains only vertices whose incident edges are

            still not covered by existing cliques; create new cliques

            to cover remaining edges until set W becomes empty */

         while (W->size > 0)

         {  /* find clique C[m], 1 <= m <= k, which shares maximal

               number of vertices with W; to break ties choose clique

               having smallest number m */

            m = 0, best = -1;

            k = H->nv - n;

            for (t = 1; t <= k; t++)

            {  /* compute cardinality of intersection of W and C[t] */

               card = 0;

               for (a = H->v[n + t]->in; a != NULL; a = a->h_next)

               {  j = a->tail->i;

                  if (W->pos[j] != 0) card++;

               }

               if (best < card)

                  m = t, best = card;

            }

            xassert(m > 0);

            /* set k := k + 1 and create new clique:

               C[k] := (W intersect C[m]) union { i }, which covers all

               edges incident to vertices from (W intersect C[m]) */

            k = glp_add_vertices(H, 1) - n;

            for (a = H->v[n + m]->in; a != NULL; a = a->h_next)

            {  j = a->tail->i;

               if (W->pos[j] != 0)

               {  /* vertex j is in both W and C[m]; include it in new

                     clique C[k] */

                  glp_add_arc(H, j, n + k);

                  /* remove vertex j from W, since edge (i,j) will be

                     covered by new clique C[k] */

                  if (W->pos[j] != W->size)

                  {  int jj = W->list[W->size];

                     W->list[W->pos[j]] = jj;

                     W->pos[jj] = W->pos[j];

                  }

                  W->size--, W->pos[j] = 0;

               }

            }

            /* include vertex i to new clique C[k] to cover edges (i,j)

               incident to all vertices j just removed from W */

            glp_add_arc(H, i, n + k);

         }

      }

      /* free working arrays */

      xfree(W->list);

      xfree(W->pos);

      xfree(V->list);

      xfree(V->pos);

      /* return the number of cliques in the edge covering found */

      return H->nv - n;

}

/* eof */