public static bool klv_init(bilist ***lbucket_ptr, /* space for left bucket sorts */ bilist ***rbucket_ptr, /* space for right bucket sorts */ bilist **llistspace, /* space for elements of linked lists */ bilist **rlistspace, /* space for elements of linked lists */ int **ldvals, /* change in separator for left moves */ int **rdvals, /* change in separator for right moves */ int nvtxs, /* number of vertices in the graph */ int maxchange /* maximum change by moving a vertex */ ) { int sizeb; /* size of set of buckets */ int sizel; /* size of set of pointers for all vertices */ /* Allocate appropriate data structures for buckets, and listspace. */ sizeb = (2 * maxchange + 1) * sizeof(bilist *); *lbucket_ptr = (bilist **)Marshal.AllocHGlobal(sizeb); *rbucket_ptr = (bilist **)Marshal.AllocHGlobal(sizeb); *ldvals = (int *)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(int)); *rdvals = (int *)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(int)); sizel = (nvtxs + 1) * sizeof(bilist); *llistspace = (bilist *)Marshal.AllocHGlobal(sizel); *rlistspace = (bilist *)Marshal.AllocHGlobal(sizel); return(*lbucket_ptr == null || *rbucket_ptr == null || *ldvals == null || *rdvals == null || *llistspace == null || *rlistspace == null); }
private static void p1bucket(bilist **bucket, /* buckets holding bucket list */ bilist *lptr, /* elements within bucket */ int maxdeg /* maximum degree of a vertex */ ) { bilist *bptr; /* loops through list at a bucket */ int val; /* element in a bucket */ int size; /* array spacing */ int i; /* loop counter */ size = (int)(&(lptr[1]) - &(lptr[0])); for (i = 2 * maxdeg; i >= 0; i--) { if (bucket[i] != null) { Console.Write(" Bucket {0:d}:", i - maxdeg); for (bptr = bucket[i]; bptr != null; bptr = bptr->next) { val = ((int)(bptr - lptr)) / size; Console.Write(" {0:d}", val); } Console.WriteLine(); } } }
/*static void p1bucket();*/ private static void pbuckets(bilist ****buckets, /* pointers to bucket lists */ bilist **listspace, /* elements within buckets */ int maxdeg, /* maximum degree of a vertex */ int nsets /* number of sets being divided into */ ) { bilist *lptr; /* points to correct listspace */ int i, j; /* loop counter */ Console.WriteLine(); for (i = 0; i < nsets; i++) { for (j = 0; j < nsets; j++) { if (i != j) { Console.WriteLine("For transition {0:d} -> {1:d}", i, j); if (j > i) { lptr = listspace[j - 1]; } else { lptr = listspace[j]; } p1bucket(buckets[i][j], lptr, maxdeg); Console.WriteLine(); } } } Console.WriteLine(); }
public static void movebilist(bilist *lptr, /* ptr to element to move */ bilist **oldlist, /* head of list to remove it from */ bilist **newlist /* head of list to add it to */ ) /* Move an element from a old bidirectional list to new one. */ { removebilist(lptr, oldlist); add2bilist(lptr, newlist); }
/* Note: bi-directional lists aren't assumed to be sorted. */ private static void add2bilist( /* add val to unsorted list */ bilist *lptr, /* element to add */ bilist **list /* list added to */ ) { lptr->next = *list; if (*list != null) { (*list)->prev = lptr; } lptr->prev = null; *list = lptr; }
static void free_kl( /* Free everything malloc'd for KL. */ bilist ****buckets, /* space for bucket sorts */ bilist **listspace, /* space for all bidirectional elements */ int **dvals, /* change in penalty for each possible move */ int **tops /* starting dval for each type of move */ ) { Marshal.FreeHGlobal((IntPtr)dvals); Marshal.FreeHGlobal((IntPtr)tops); Marshal.FreeHGlobal((IntPtr)listspace[0]); Marshal.FreeHGlobal((IntPtr)buckets[0][1]); Marshal.FreeHGlobal((IntPtr)listspace); Marshal.FreeHGlobal((IntPtr)buckets); }
public static void free_klv( /* Free everything malloc'd for KLV. */ bilist **lbuckets, /* space for bucket sorts */ bilist **rbuckets, /* space for bucket sorts */ bilist *llistspace, /* space for all bidirectional elements */ bilist *rlistspace, /* space for all bidirectional elements */ int *ldvals, /* change in penalty for each possible move */ int *rdvals /* change in penalty for each possible move */ ) { Marshal.FreeHGlobal((IntPtr)rlistspace); Marshal.FreeHGlobal((IntPtr)llistspace); Marshal.FreeHGlobal((IntPtr)rdvals); Marshal.FreeHGlobal((IntPtr)ldvals); Marshal.FreeHGlobal((IntPtr)rbuckets); Marshal.FreeHGlobal((IntPtr)lbuckets); }
private static void removebilist(bilist *lptr, /* ptr to element to remove */ bilist **list /* head of list to remove it from */ ) /* Remove an element from a bidirectional list. */ { if (lptr->next != null) { lptr->next->prev = lptr->prev; } if (lptr->prev != null) { lptr->prev->next = lptr->next; } else { *list = lptr->next; } }
/* Idea: * 'buckets[i][j]' is a set of buckets to sort moves from i to j. * listspace[i] is space for lists in buckets[i][j]. * Loop through all nonequal pairs [i][j], taking the first element * in each list. Compare them all to find the largest allowed move. * Make that move, and save it in movelist. */ public static void bucketsort1(vtx_data **graph, /* graph data structure */ int vtx, /* vertex being added to lists */ bilist ****buckets, /* array of lists for bucket sort */ bilist **listspace, /* list data structure for each vertex */ int **dvals, /* d-values for each vertex for removing */ int *sets, /* processor each vertex is assigned to */ float *[] term_wgts, /* weights for terminal propagation */ int maxdval, /* maximum possible dvalue for a vertex */ int nsets, /* number of sets being divided into */ int [][] hops, /* hop cost between sets */ bool useEdgeWeights /* are edge weights being used? */ ) { bilist *lptr = null; /* pointer to an element in listspace */ float * ewptr = null; /* loops through edge weights */ int * edges = null; /* edge list for a vertex */ int myset; /* set that current vertex belongs to */ int newset; /* set current vertex could move to */ int set; /* set that neighboring vertex belongs to */ int weight; /* edge weight for a particular edge */ float tval; /* terminal propagation value */ int val; /* terminal propagation rounded value */ double cut_cost; /* relative cut/hop importance */ double hop_cost; /* relative hop/cut importance */ int myhop; /* hops associated with current vertex */ int j, l; /* loop counters */ /* Compute d-vals by seeing which sets neighbors belong to. */ cut_cost = hop_cost = 1; if (term_wgts[1] != null) { if (CUT_TO_HOP_COST > 1) { cut_cost = CUT_TO_HOP_COST; } else { hop_cost = 1.0 / CUT_TO_HOP_COST; } } weight = (int)(cut_cost + .5); myset = sets[vtx]; /* Initialize all the preference values. */ if (term_wgts[1] != null) { /* Using terminal propagation. */ if (myset == 0) /* No terminal value. */ { for (newset = 1; newset < nsets; newset++) { tval = (term_wgts[newset])[vtx]; if (tval < 0) { val = (int)(-tval * hop_cost + .5); val = -val; } else { val = (int)(tval * hop_cost + .5); } dvals[vtx][newset - 1] = val; } } else { tval = -(term_wgts[myset])[vtx]; if (tval < 0) { val = (int)(-tval * hop_cost + .5); val = -val; } else { val = (int)(tval * hop_cost + .5); } dvals[vtx][0] = val; l = 1; for (newset = 1; newset < nsets; newset++) { if (newset != myset) { tval = (term_wgts[newset])[vtx] - (term_wgts[myset])[vtx]; if (tval < 0) { val = (int)(-tval * hop_cost + .5); val = -val; } else { val = (int)(tval * hop_cost + .5); } dvals[vtx][l] = val; l++; } } } } else { for (j = 0; j < nsets - 1; j++) { dvals[vtx][j] = 0; } } /* First count the neighbors in each set. */ edges = graph[vtx]->edges; if (useEdgeWeights) { ewptr = graph[vtx]->ewgts; } for (j = graph[vtx]->nedges - 1; j != 0; j--) { set = sets[*(++edges)]; if (set < 0) { set = -set - 1; } if (useEdgeWeights) { weight = (int)(*(++ewptr) * cut_cost + .5); } myhop = hops[myset][set]; l = 0; for (newset = 0; newset < nsets; newset++) { if (newset != myset) { dvals[vtx][l] += weight * (myhop - hops[newset][set]); l++; } } } /* Now add to appropriate buckets. */ l = 0; for (newset = 0; newset < nsets; newset++) { if (newset != myset) { lptr = listspace[l]; add2bilist(&lptr[vtx], &buckets[myset][newset][dvals[vtx][l] + maxdval]); ++l; } } }
/* Idea: * 'buckets[i][j]' is a set of buckets to sort moves from i to j. * listspace[i] is space for lists in buckets[i][j]. * Loop through all nonequal pairs [i][j], taking the first element * in each list. Compare them all to find the largest allowed move. * Make that move, and save it in movelist. */ /* Routine slightly streamlined for case with only two sets. */ public static void bucketsorts_bi(vtx_data **graph, /* graph data structure */ int nvtxs, /* number of vertices */ bilist ****buckets, /* array of lists for bucket sort */ bilist **listspace, /* list data structure for each vertex */ int **dvals, /* d-values for each vertex for removing */ int *sets, /* processor each vertex is assigned to */ float *[] term_wgts, /* weights for terminal propagation */ int maxdval, /* maximum possible dvalue for a vertex */ int nsets, /* number of sets being divided into */ bool parity, /* work in forward or backward direction? */ int [][] hops, /* hop cost between sets */ int *bspace, /* indices for randomly ordering vtxs */ int list_length, /* number of values in bspace to work with */ int npass, /* which pass through KL is this? */ bool useEdgeWeights /* are edge weights being used? */ ) { bilist **bptr = null; /* loops through set of buckets */ bilist * lptr = null; /* pointer to an element in listspace */ float * ewptr = null; /* loops through edge weights */ float * twptr = null; /* weights for terminal propagation */ int * bsptr = null; /* loops through bspace */ int * edges = null; /* edge list for a vertex */ int myset; /* set current vertex belongs to */ int other_set; /* set current vertex doesn't belong to */ int set; /* set that neighboring vertex belongs to */ int weight; /* edge weight for a particular edge */ int vtx; /* vertex in graph */ int val; /* terminal propagation rounded value */ double cut_cost; /* relative cut/hop importance */ double hop_cost; /* relative hop/cut importance */ int myhop; /* hops associated with current vertex */ int i, j; /* loop counters */ /* For each vertex, compute d-values for each possible transition. */ /* Then store them in each appropriate bucket. */ if (npass == 1 || !KL_UNDO_LIST || list_length == nvtxs) { /* Empty all the buckets. */ /* Last clause catches case where lists weren't undone. */ bptr = buckets[0][1]; for (i = nsets * (nsets - 1) * (2 * maxdval + 1); i != 0; i--) { *bptr++ = null; } } /* Randomize the order of the vertices */ if ((KL_UNDO_LIST && list_length == nvtxs) || !KL_UNDO_LIST) { list_length = nvtxs; bsptr = bspace; if (parity) { for (i = 1; i <= nvtxs; i++) { *bsptr++ = i; } } else { for (i = nvtxs; i != 0; i--) { *bsptr++ = i; } } } if (KL_RANDOM) { randomize(bspace - 1, list_length); } /* Now compute d-vals by seeing which sets neighbors belong to. */ cut_cost = hop_cost = 1; if (term_wgts[1] != null) { if (CUT_TO_HOP_COST > 1) { cut_cost = CUT_TO_HOP_COST; } else { hop_cost = 1.0 / CUT_TO_HOP_COST; } } weight = (int)(cut_cost + .5); bsptr = bspace; twptr = term_wgts[1]; for (i = 0; i < list_length; i++) /* Loop through vertices. */ { vtx = *bsptr++; myset = sets[vtx]; other_set = myset == 0 ? 1 : 0; /* Initialize all the preference values. */ if (twptr != null) { /* Using terminal propagation. Round to integer value. */ if (twptr[vtx] < 0) { val = (int)(-twptr[vtx] * hop_cost + .5); val = -val; } else { val = (int)(twptr[vtx] * hop_cost + .5); } if (myset == 0) { dvals[vtx][0] = val; } else { dvals[vtx][0] = -val; } } else { dvals[vtx][0] = 0; } /* First count the neighbors in each set. */ edges = graph[vtx]->edges; if (useEdgeWeights) { ewptr = graph[vtx]->ewgts; } for (j = graph[vtx]->nedges - 1; j != 0; j--) { set = sets[*(++edges)]; if (set < 0) { set = -set - 1; } if (useEdgeWeights) { weight = (int)((*(++ewptr)) * cut_cost + .5); } myhop = hops[myset][set]; dvals[vtx][0] += weight * (myhop - hops[other_set][set]); } /* Now add to appropriate buckets. */ lptr = listspace[0]; add2bilist(&lptr[vtx], &buckets[myset][other_set][dvals[vtx][0] + maxdval]); } }
public static void bucketsortsv(vtx_data **graph, /* graph data structure */ int nvtxs, /* number of vertices */ bilist **lbuckets, /* array of lists for bucket sort */ bilist **rbuckets, /* array of lists for bucket sort */ bilist *llistspace, /* list data structure for each vertex */ bilist *rlistspace, /* list data structure for each vertex */ int *ldvals, /* d-values for each vertex for removing */ int *rdvals, /* d-values for each vertex for removing */ int *sets, /* processor each vertex is assigned to */ int maxdval, /* maximum possible dvalue for a vertex */ bool parity, /* work in forward or backward direction? */ int *bspace, /* indices for randomly ordering vtxs */ int list_length /* number of values in bspace to work with */ ) { bilist **lbptr; /* loops through set of buckets */ bilist **rbptr; /* loops through set of buckets */ int * bsptr; /* loops through bspace */ int * edges; /* edge list for a vertex */ int left_weight; /* my neighbors in 0 set */ int right_weight; /* my neighbors in 1 set */ int vtx; /* vertex in graph */ int neighbor; /* neighbor of vertex */ int set; /* set that neighboring vertex belongs to */ int i, j; /* loop counters */ /* For each vertex, compute d-values and store in buckets. */ /* Empty all the buckets. */ rbptr = lbuckets; lbptr = rbuckets; for (i = (2 * maxdval + 1); i != 0; i--) { *lbptr++ = null; *rbptr++ = null; } /* Randomize the order of the vertices */ if ((KL_UNDO_LIST && list_length == nvtxs) || (!KL_UNDO_LIST && !KL_RANDOM) || list_length == 0) { /* Don't need to reoder if about to randomize. */ list_length = nvtxs; bsptr = bspace; if (parity) { for (i = 1; i <= nvtxs; i++) { *bsptr++ = i; } } else { for (i = nvtxs; i != 0; i--) { *bsptr++ = i; } } } if (KL_RANDOM) { randomize(bspace - 1, list_length); } /* Now compute d-vals by seeing which sets neighbors belong to. */ bsptr = bspace; for (i = 0; i < list_length; i++) { /* Loop through vertices. */ vtx = *bsptr++; if (sets[vtx] == 2) { /* Only worry about separator vertices. */ /* Initialize all the preference values. */ left_weight = right_weight = 0; /* First count the neighbors in each set. */ edges = graph[vtx]->edges; for (j = graph[vtx]->nedges - 1; j != 0; j--) { neighbor = *(++edges); set = sets[neighbor]; if (set < 0) { set = -set - 1; } if (set == 0) { left_weight += graph[neighbor]->vwgt; } else if (set == 1) { right_weight += graph[neighbor]->vwgt; } } ldvals[vtx] = graph[vtx]->vwgt - right_weight; rdvals[vtx] = graph[vtx]->vwgt - left_weight; /* Now add to appropriate buckets. */ add2bilist(&llistspace[vtx], &lbuckets[ldvals[vtx] + maxdval]); add2bilist(&rlistspace[vtx], &rbuckets[rdvals[vtx] + maxdval]); } } }
public static void make_bndy_list(vtx_data **graph, /* data structure for graph */ bilist *movelist, /* list of vtxs to be moved */ bilist ****buckets, /* array of lists for bucket sort */ bilist **listspace, /* list data structure for each vertex */ int *sets, /* processor each vertex is assigned to */ int nsets, /* number of sets divided into */ int *bspace, /* list of active vertices for bucketsort */ int **tops, /* top of each set of buckets */ int **bndy_list /* list of boundary vertices returned */ ) { bilist *bptr; /* loops through bspace */ int vtx; /* vertex that was moved */ int set; /* set a vertex is in */ int list_length; /* number of active vertices */ int bndy_length; /* number of vertices actually on boundary */ int size; /* array spacing */ int i, j, k; /* loop counters */ /* First push all the moved vertices onto list, so they can be flagged. */ /* They've already been removed from buckets, so want to avoid them. */ size = (int)(&(listspace[0][1]) - &(listspace[0][0])); bptr = movelist; list_length = 0; while (bptr != null) { vtx = ((int)(bptr - listspace[0])) / size; bspace[list_length++] = vtx; bptr = bptr->next; } /* Now get all the vertices still in the bucket lists. */ for (k = tops[0][1]; k >= 0; k--) { bptr = buckets[0][1][k]; while (bptr != null) { vtx = ((int)(bptr - listspace[0])) / size; bspace[list_length++] = vtx; bptr = bptr->next; } } for (i = 1; i < nsets; i++) { for (k = tops[i][0]; k >= 0; k--) { bptr = buckets[i][0][k]; while (bptr != null) { vtx = ((int)(bptr - listspace[0])) / size; bspace[list_length++] = vtx; bptr = bptr->next; } } } /* Now that list is constructed, go reconstruct all the set numbers. */ bndy_length = 0; for (i = 0; i < list_length; i++) { vtx = bspace[i]; set = sets[vtx]; for (j = 1; j < graph[vtx]->nedges; j++) { if (sets[graph[vtx]->edges[j]] != set) { bspace[bndy_length++] = vtx; break; } } } /* Finally, copy boundary vertices into boundary list. */ *bndy_list = (int *)Marshal.AllocHGlobal((bndy_length + 1) * sizeof(int)); for (i = 0; i < bndy_length; i++) { (*bndy_list)[i] = bspace[i]; } (*bndy_list)[bndy_length] = 0; }
private static void p1bucket(bilist **a, bilist *b, int c) { throw new NotImplementedException("I couldn't find the implementation for this in Chaco source."); }
/* * Keep guys moved in and guys moving out of separator. * To restore, move all undesirable guys back. * (1) guys moved out of separator get put back in. * (2) guys moved into separator (bspace) get put back. * Note: Should be done in this order. * Note: No neighbors need be considered. * (3) To clear dvals, I should compute touch all guys that * were ever in separator (bspace) and their neighbors. */ public static bool nway_klv(vtx_data **graph, /* data structure for graph */ int nvtxs, /* number of vtxs in graph */ bilist **lbuckets, /* array of lists for bucket sort */ bilist **rbuckets, /* array of lists for bucket sort */ bilist *llistspace, /* list data structure for each vertex */ bilist *rlistspace, /* list data structure for each vertex */ int *ldvals, /* d-values for each transition */ int *rdvals, /* d-values for each transition */ int *sets, /* processor each vertex is assigned to */ int maxdval, /* maximum d-value for a vertex */ double[] goal, /* desired set sizes */ int max_dev, /* largest allowed deviation from balance */ int **bndy_list, /* list of vertices on boundary (0 ends) */ double[] weightsum /* sum of vweights in each set (in and out) */ ) { bilist **to_buckets; /* buckets I'm moving to */ bilist **from_buckets; /* buckets I'm moving from */ bilist * to_listspace; /* list structure I'm moving to */ bilist * from_listspace; /* list structure I'm moving from */ bilist * out_list; /* list of vtxs moved out of separator */ int * to_dvals; /* d-values I'm moving to */ int * from_dvals; /* d-values I'm moving from */ int * bspace; /* list of active vertices for bucketsort */ int * edges; /* edge list for a vertex */ int * edges2; /* edge list for a vertex */ int * bdy_ptr; /* loops through bndy_list */ double total_weight; /* weight of all vertices */ double partial_weight; /* weight of vertices not in separator */ double ratio; /* fraction of weight not in separator */ double time; /* timing parameter */ double delta0; /* largest negative deviation from goal size */ double delta1; /* largest negative deviation from goal size */ double left_imbalance = 0.0; /* imbalance if I move to the left */ double right_imbalance; /* imbalance if I move to the right */ double balance_val; /* how imbalanced is it */ double balance_best; /* best balance yet if trying hard */ bool flag; /* condition indicator */ int to = -1, from; /* sets moving into / out of */ int rtop, ltop; /* top of each set of buckets */ int * to_top; /* ptr to top of set moving to */ int lvtx, rvtx; /* next vertex to move left/right */ int lweight, rweight; /* weights of moving vertices */ int weightfrom = 0; /* weight moving out of a set */ int list_length; /* how long is list of vertices to bucketsort? */ bool balanced; /* is partition balanced? */ bool temp_balanced; /* is intermediate partition balanced? */ bool ever_balanced; /* has any partition been balanced? */ int bestvtx = -1; /* best vertex to move */ int bestval = -1; /* best change in value for a vtx move */ int vweight; /* weight of best vertex */ int gtotal; /* sum of changes from moving */ int improved; /* total improvement from KL */ double bestg; /* maximum gtotal found in KL loop */ double bestg_min; /* smaller than any possible bestg */ int beststep; /* step where maximum value occurred */ int bestlength; /* step where maximum value occurred */ int neighbor; /* neighbor of a vertex */ int step_cutoff; /* number of negative steps in a row allowed */ int cost_cutoff; /* amount of negative d-values allowed */ int neg_steps; /* number of negative steps in a row */ int neg_cost; /* decrease in sum of d-values */ int vtx; /* vertex number */ int dval; /* dval of a vertex */ int group, group2; /* set that a vertex is assigned to */ bool left_too_big; /* is left set too large? */ bool right_too_big; /* is right set too large? */ int vwgt; /* weight of a vertex */ int gain; /* reduction in separator due to a move */ int neighbor2; /* neighbor of a vertex */ int step; /* loops through movements of vertices */ bool parity; /* sort forwards or backwards? */ bool done; /* has termination criteria been achieved? */ int nbad; /* number of unhelpful passes in a row */ int npass; /* total number of passes */ int nbadtries; /* number of unhelpful passes before quitting */ bool enforce_balance; /* force a balanced partition? */ bool enforce_balance_hard; /* really force a balanced partition? */ int i, j, k; /* loop counters */ nbadtries = KL_NTRIES_BAD; enforce_balance = false; enforce_balance_hard = false; total_weight = goal[0] + goal[1]; bspace = (int *)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(int)); if (bspace == null) { return(true); } bdy_ptr = *bndy_list; list_length = 0; while (*bdy_ptr != 0) { bspace[list_length++] = *bdy_ptr++; } Marshal.FreeHGlobal((IntPtr)(*bndy_list)); clear_dvals(graph, nvtxs, ldvals, rdvals, bspace, list_length); step_cutoff = KL_BAD_MOVES; cost_cutoff = maxdval * step_cutoff / 7; if (cost_cutoff < step_cutoff) { cost_cutoff = step_cutoff; } partial_weight = weightsum[0] + weightsum[1]; ratio = partial_weight / total_weight; delta0 = Math.Abs(weightsum[0] - goal[0] * ratio); delta1 = Math.Abs(weightsum[1] - goal[1] * ratio); balanced = (delta0 + delta1 <= max_dev) && weightsum[0] != total_weight && weightsum[1] != total_weight; bestg_min = -2.0 * nvtxs * maxdval; parity = false; nbad = 0; npass = 0; improved = 0; done = false; while (!done) { npass++; ever_balanced = false; balance_best = delta0 + delta1; /* Initialize various quantities. */ ltop = rtop = 2 * maxdval; gtotal = 0; bestg = bestg_min; beststep = -1; bestlength = list_length; out_list = null; neg_steps = 0; /* Compute the initial d-values, and bucket-sort them. */ time = seconds(); bucketsortsv(graph, nvtxs, lbuckets, rbuckets, llistspace, rlistspace, ldvals, rdvals, sets, maxdval, parity, bspace, list_length); parity = !parity; kl_bucket_time += seconds() - time; if (DEBUG_KL == DebugFlagKL.PrintBucket) { Console.WriteLine("After sorting, left buckets:"); p1bucket(lbuckets, llistspace, maxdval); Console.WriteLine(" right buckets:"); p1bucket(rbuckets, rlistspace, maxdval); } /* Now determine the set of vertex moves. */ for (step = 1;; step++) { /* Find the highest d-value in each set. */ /* But only consider moves from large to small sets, or moves */ /* in which balance is preserved. */ /* Break ties in some nonarbitrary manner. */ bestval = -maxdval - 1; partial_weight = weightsum[0] + weightsum[1]; ratio = partial_weight / total_weight; left_too_big = (weightsum[0] > (goal[0] + .5 * max_dev) * ratio); right_too_big = (weightsum[1] > (goal[1] + .5 * max_dev) * ratio); while (ltop >= 0 && lbuckets[ltop] == null) { --ltop; } if (ltop >= 0 && !left_too_big) { lvtx = (int)(((long)lbuckets[ltop] - (long)llistspace) / sizeof(bilist)); lweight = graph[lvtx]->vwgt; rweight = lweight - (ltop - maxdval); weightfrom = rweight; to = 0; bestvtx = lvtx; bestval = ltop - maxdval; partial_weight = weightsum[0] + lweight + weightsum[1] - rweight; ratio = partial_weight / total_weight; left_imbalance = Math.Max(Math.Abs(weightsum[0] + lweight - goal[0] * ratio), Math.Abs(weightsum[1] - rweight - goal[1] * ratio)); } while (rtop >= 0 && rbuckets[rtop] == null) { --rtop; } if (rtop >= 0 && !right_too_big) { rvtx = (int)(((long)rbuckets[rtop] - (long)rlistspace) / sizeof(bilist)); rweight = graph[rvtx]->vwgt; lweight = rweight - (rtop - maxdval); partial_weight = weightsum[0] - lweight + weightsum[1] + rweight; ratio = partial_weight / total_weight; right_imbalance = Math.Max(Math.Abs(weightsum[0] - lweight - goal[0] * ratio), Math.Abs(weightsum[1] + rweight - goal[1] * ratio)); if (rtop - maxdval > bestval || (rtop - maxdval == bestval && (right_imbalance < left_imbalance || (right_imbalance == left_imbalance && drandom() < .5)))) { to = 1; weightfrom = lweight; bestvtx = rvtx; bestval = rtop - maxdval; } } if (bestval == -maxdval - 1) { /* No allowed moves */ if (DEBUG_KL != DebugFlagKL.NoDebugging) { Console.WriteLine("No KLV moves at step {0:d}. bestg = {1:g} at step {2:d}.", step, bestg, beststep); } break; } if (to == 0) { from = 1; to_listspace = llistspace; from_listspace = rlistspace; to_dvals = ldvals; from_dvals = rdvals; to_buckets = lbuckets; from_buckets = rbuckets; to_top = <op; } else { from = 0; to_listspace = rlistspace; from_listspace = llistspace; to_dvals = rdvals; from_dvals = ldvals; to_buckets = rbuckets; from_buckets = lbuckets; to_top = &rtop; } vweight = graph[bestvtx]->vwgt; weightsum[to] += vweight; weightsum[from] -= weightfrom; /* Check if this partition is balanced. */ partial_weight = weightsum[0] + weightsum[1]; ratio = partial_weight / total_weight; delta0 = Math.Abs(weightsum[0] - goal[0] * ratio); delta1 = Math.Abs(weightsum[1] - goal[1] * ratio); temp_balanced = (delta0 + delta1 <= max_dev) && weightsum[0] != total_weight && weightsum[1] != total_weight; ever_balanced = (ever_balanced || temp_balanced); balance_val = delta0 + delta1; gtotal += bestval; if ((gtotal > bestg && temp_balanced) || (enforce_balance_hard && balance_val < balance_best)) { bestg = gtotal; beststep = step; if (balance_val < balance_best) { balance_best = balance_val; } if (temp_balanced) { enforce_balance_hard = false; } } if (DEBUG_KL == DebugFlagKL.MoreInfo || DEBUG_KL == DebugFlagKL.PrintBucket) { Console.WriteLine("At KLV step {0:d}, bestvtx={1:d}, bestval={2:d} (2->{3:d}), wt0 = {4:g,} wt1 = {5:g}", step, bestvtx, bestval, to, weightsum[0], weightsum[1]); } /* Monitor the stopping criteria. */ if (bestval < 0) { if (!enforce_balance || ever_balanced) { neg_steps++; } if (bestg != bestg_min) { neg_cost = (int)bestg - gtotal; } else { neg_cost = -maxdval - 1; } if ((neg_steps > step_cutoff || neg_cost > cost_cutoff) && !(enforce_balance && bestg == bestg_min)) { if (DEBUG_KL != DebugFlagKL.NoDebugging) { if (neg_steps > step_cutoff || neg_cost > cost_cutoff) { Console.WriteLine("KLV step cutoff at step {0:d}. bestg = {1:g} at step {2:d}.", step, bestg, beststep); } } weightsum[to] -= vweight; weightsum[from] += weightfrom; break; } } else if (bestval > 0) { neg_steps = 0; } /* Remove vertex from its buckets, and flag it as finished. */ sets[bestvtx] = to; removebilist(&to_listspace[bestvtx], &to_buckets[bestval + maxdval]); /* * printf("After to removebilist\n"); * p1bucket(to_buckets, to_listspace, maxdval); */ if (from_dvals[bestvtx] != -maxdval - 1) { removebilist(&from_listspace[bestvtx], &from_buckets[from_dvals[bestvtx] + maxdval]); /* * printf("After from removebilist\n"); * p1bucket(from_buckets, from_listspace, maxdval); */ } from_dvals[bestvtx] = -maxdval - 1; /* Now keep track of vertices moved out of separator so */ /* I can restore them as needed. */ llistspace[bestvtx].next = out_list; out_list = &(llistspace[bestvtx]); /* Now update the d-values of all the neighbors */ /* And neighbors of neighbors ... */ /* If left move: * 1. Separator neighbors right gain => infinity * 2. Left neighbors unaffected. * 3. Right neighbors move into separator. * A. Right gain = infinity. * B. Left gain = computed. * C. For any of their neighbors in separator increase left gain. */ edges = graph[bestvtx]->edges; for (j = graph[bestvtx]->nedges - 1; j != 0; j--) { neighbor = *(++edges); group = sets[neighbor]; if (group == 2) { /* In separator. */ gain = from_dvals[neighbor] + maxdval; /* Gain in the from direction => -infinity */ if (gain >= 0) { removebilist(&from_listspace[neighbor], &from_buckets[gain]); /* * printf("\n After removing %d\n", neighbor); * p1bucket(from_buckets, from_listspace, maxdval); */ from_dvals[neighbor] = -maxdval - 1; } } else if (group == from) { /* Gain in the from direction => -infinity */ sets[neighbor] = 2; from_dvals[neighbor] = -maxdval - 1; if (to == 0) { bspace[list_length++] = -neighbor; } else { bspace[list_length++] = neighbor; } edges2 = graph[neighbor]->edges; vwgt = graph[neighbor]->vwgt; gain = graph[neighbor]->vwgt; flag = false; for (k = graph[neighbor]->nedges - 1; k != 0; k--) { neighbor2 = *(++edges2); group2 = sets[neighbor2]; if (group2 == 2) { dval = to_dvals[neighbor2] + maxdval; if (dval >= 0) { movebilist(&to_listspace[neighbor2], &to_buckets[dval], &to_buckets[dval + vwgt]); /* * printf("\n After moving %d from bucket %d to bucket * %d\n", neighbor2, dval, dval + vwgt); * p1bucket(to_buckets, to_listspace, maxdval); */ to_dvals[neighbor2] += vwgt; dval += vwgt; if (dval > *to_top) { *to_top = dval; } } } else if (group2 == from) { gain -= graph[neighbor2]->vwgt; if (to_dvals[neighbor2] + maxdval < 0) { flag = true; } } } if (flag) { /* Not allowed to move further. */ to_dvals[neighbor] = -maxdval - 1; } else { to_dvals[neighbor] = gain; /* place in appropriate bucket */ gain += maxdval; add2bilist(&to_listspace[neighbor], &to_buckets[gain]); /* * printf("\nAfter adding %d to bucket %d\n", neighbor, gain - * maxdval); * p1bucket(to_buckets, to_listspace, maxdval); */ if (gain > *to_top) { *to_top = gain; } } } } if (beststep == step) { bestlength = list_length; } if (DEBUG_KL == DebugFlagKL.PrintBucket) { Console.WriteLine("\n-- After step, left buckets:"); p1bucket(lbuckets, llistspace, maxdval); Console.WriteLine(" right buckets:"); p1bucket(rbuckets, rlistspace, maxdval); } } /* Done with a pass; should we actually perform any swaps? */ if (bestg > 0 || (bestg != bestg_min && !balanced && enforce_balance)) { improved += (int)bestg; } else { if (enforce_balance_hard) { /* I've done the best I can, give up. */ done = true; } if (enforce_balance) { enforce_balance_hard = true; } enforce_balance = true; nbad++; } /* Work backwards, undoing all the undesirable moves. */ /* First reset vertices moved out of the separator. */ if (out_list != null) { if (beststep < 0) { beststep = 0; } for (i = step - 1; i > beststep; i--) { vtx = (int)(((long)out_list - (long)llistspace) / sizeof(bilist)); if (sets[vtx] != 2) { weightsum[sets[vtx]] -= graph[vtx]->vwgt; } sets[vtx] = 2; out_list = out_list->next; } } for (i = list_length - 1; i >= bestlength; i--) { vtx = bspace[i]; if (vtx < 0) { if (sets[-vtx] == 2) { weightsum[1] += graph[-vtx]->vwgt; } sets[-vtx] = 1; } else { if (sets[vtx] == 2) { weightsum[0] += graph[vtx]->vwgt; } sets[vtx] = 0; } } partial_weight = weightsum[0] + weightsum[1]; ratio = partial_weight / total_weight; delta0 = Math.Abs(weightsum[0] - goal[0] * ratio); delta1 = Math.Abs(weightsum[1] - goal[1] * ratio); balanced = (delta0 + delta1 <= max_dev) && weightsum[0] != total_weight && weightsum[1] != total_weight; done = done || (nbad >= nbadtries && balanced); if (KL_MAX_PASS > 0) { done = done || (npass == KL_MAX_PASS && balanced); } if (!done) { /* Rezero dval values. */ clear_dvals(graph, nvtxs, ldvals, rdvals, bspace, list_length); } /* Construct list of separator vertices to pass to buckets or return */ list_length = make_sep_list(bspace, list_length, sets); if (done) { bspace[list_length] = 0; bspace = (int *)Marshal.ReAllocHGlobal((IntPtr)bspace, new IntPtr((list_length + 1) * sizeof(int))); *bndy_list = bspace; } gain = 0; j = k = 0; for (i = 1; i <= nvtxs; i++) { if (sets[i] == 0) { j += graph[i]->vwgt; } else if (sets[i] == 1) { k += graph[i]->vwgt; } else if (sets[i] == 2) { gain += graph[i]->vwgt; } } /* * printf("\nAfter pass of KLV: sets = %d/%d, sep = %d (bestg = %g)\n\n\n", j, k, gain, bestg); */ } if (DEBUG_KL != DebugFlagKL.NoDebugging) { Console.WriteLine(" KLV required {0:d} passes to improve by {1:d}.", npass, improved); } return(false); }
private static int make_kl_list(vtx_data **graph, /* data structure for graph */ bilist *movelist, /* list of vtxs to be moved */ bilist ****buckets, /* array of lists for bucket sort */ bilist **listspace, /* list data structure for each vertex */ int *sets, /* processor each vertex is assigned to */ int nsets, /* number of sets divided into */ int *bspace, /* list of active vertices for bucketsort */ int **dvals, /* d-values for each transition */ int maxdval /* maximum d-value for a vertex */ ) { bilist **list; /* bucket to erase element from */ bilist * vptr; /* loops through movelist */ int * bptr; /* loops through bspace */ int * iptr; /* loops through edge list */ int vtx; /* vertex that was moved */ int neighbor; /* neighbor of a vertex */ int myset; /* set a vertex is in */ int newset; /* loops through other sets */ int list_length; /* number of values put in bspace */ int size; /* array spacing */ int i, l; /* loop counter */ /* First push all the moved vertices onto list, so they can be flagged. */ /* They've already been removed from buckets, so want to avoid them. */ size = (int)(&(listspace[0][1]) - &(listspace[0][0])); vptr = movelist; bptr = bspace; list_length = 0; while (vptr != null) { vtx = ((int)(vptr - listspace[0])) / size; *bptr++ = vtx; if (sets[vtx] >= 0) { sets[vtx] = -sets[vtx] - 1; } ++list_length; vptr = vptr->next; } /* Now look at all the neighbors of moved vertices. */ vptr = movelist; while (vptr != null) { vtx = ((int)(vptr - listspace[0])) / size; iptr = graph[vtx]->edges; for (i = graph[vtx]->nedges - 1; i != 0; i--) { neighbor = *(++iptr); if (sets[neighbor] >= 0) { *bptr++ = neighbor; ++list_length; myset = sets[neighbor]; sets[neighbor] = -sets[neighbor] - 1; /* Remove neighbor entry from all his buckets. */ /* Note: vertices in movelist already removed from buckets. */ l = 0; for (newset = 0; newset < nsets; newset++) { if (newset != myset) { list = &buckets[myset][newset][dvals[neighbor][l] + maxdval]; removebilist(&listspace[l][neighbor], list); l++; } } } } vptr = vptr->next; } /* Now that list is constructed, go reconstruct all the set numbers. */ bptr = bspace; for (i = list_length; i != 0; i--) { vtx = *bptr++; sets[vtx] = -sets[vtx] - 1; } return(list_length); }
/* Idea: * 'buckets[i][j]' is a set of buckets to sort moves from i to j. * listspace[i] is space for lists in buckets[i][j]. * Loop through all nonequal pairs [i][j], taking the first element * in each list. Compare them all to find the largest allowed move. * Make that move, and save it in movelist. */ public static bool nway_kl(vtx_data **graph, /* data structure for graph */ int nvtxs, /* number of vtxs in graph */ bilist ****buckets, /* array of lists for bucket sort */ bilist **listspace, /* list data structure for each vertex */ int **tops, /* 2-D array of top of each set of buckets */ int **dvals, /* d-values for each transition */ int *sets, /* processor each vertex is assigned to */ int maxdval, /* maximum d-value for a vertex */ int nsets, /* number of sets divided into */ double [] goal, /* desired set sizes */ float *[] term_wgts, /* weights for terminal propagation */ int [][] hops, /* cost of set transitions */ int max_dev, /* largest allowed deviation from balance */ bool useEdgeWeights, /* are edge weights being used? */ int **bndy_list, /* list of vertices on boundary (0 ends) */ double [] startweight /* sum of vweights in each set (in and out) */ ) /* Suaris and Kedem algorithm for quadrisection, generalized to an */ /* arbitrary number of sets, with intra-set cost function specified by hops. */ /* Note: this is for a single divide step. */ /* Also, sets contains an initial (possibly crummy) partitioning. */ { bilist * movelist; /* list of vtxs to be moved */ bilist **endlist; /* end of movelists */ bilist * bestptr; /* best vertex in linked list */ bilist * bptr; /* loops through bucket list */ float * ewptr = null; /* loops through edge weights */ double * locked = null; /* weight of vertices locked in a set */ double * loose = null; /* weight of vtxs that can move from a set */ int * bspace = null; /* list of active vertices for bucketsort */ double * weightsum = null; /* sum of vweights for each partition */ int * edges = null; /* edge list for a vertex */ int * bdy_ptr = null; /* loops through bndy_list */ double time; /* timing parameter */ double delta; /* desire of sets to change size */ double bestdelta = -1; /* strongest delta value */ double deltaplus; /* largest negative deviation from goal size */ double deltaminus; /* largest negative deviation from goal size */ int list_length; /* how long is list of vertices to bucketsort? */ bool balanced; /* is partition balanced? */ bool temp_balanced; /* is intermediate partition balanced? */ bool ever_balanced; /* has any partition been balanced? */ int bestvtx = -1; /* best vertex to move */ int bestval = -1; /* best change in value for a vtx move */ int bestfrom = -1, bestto = -1; /* sets best vertex moves between */ int vweight; /* weight of best vertex */ int gtotal; /* sum of changes from moving */ int improved; /* total improvement from KL */ double balance_val = 0.0; /* how imbalanced is it */ double balance_best; /* best balance yet if trying hard */ double bestg; /* maximum gtotal found in KL loop */ double bestg_min; /* smaller than any possible bestg */ int beststep; /* step where maximum value occurred */ int neighbor; /* neighbor of a vertex */ int step_cutoff; /* number of negative steps in a row allowed */ int cost_cutoff; /* amount of negative d-values allowed */ int neg_steps; /* number of negative steps in a row */ int neg_cost; /* decrease in sum of d-values */ int vtx; /* vertex number */ int dval; /* dval of a vertex */ int group; /* set that a vertex is assigned to */ double cut_cost; /* if term_prop; relative cut/hop importance */ int diff; /* change in a d-value */ int stuck1st, stuck2nd; /* how soon will moves be disallowed? */ int beststuck1 = -1, beststuck2 = -1; /* best stuck values for tie-breaking */ int eweight; /* a particular edge weight */ bool worth_undoing; /* is it worth undoing list? */ float undo_frac; /* fraction of vtxs indicating worth of undoing */ int step; /* loops through movements of vertices */ bool parity; /* sort forwards or backwards? */ bool done; /* has termination criteria been achieved? */ int nbad; /* number of unhelpful passes in a row */ int npass; /* total number of passes */ int nbadtries; /* number of unhelpful passes before quitting */ bool enforce_balance; /* force a balanced partition? */ bool enforce_balance_hard; /* really force a balanced partition? */ bool balance_trouble; /* even balance_hard isn't working */ int size; /* array spacing */ int i, j, k, l; /* loop counters */ nbadtries = KL_NTRIES_BAD; enforce_balance = false; temp_balanced = false; enforce_balance_hard = false; balance_trouble = false; size = (int)(&(listspace[0][1]) - &(listspace[0][0])); undo_frac = 0.3f; cut_cost = 1; if (term_wgts[1] != null) { if (CUT_TO_HOP_COST > 1) { cut_cost = CUT_TO_HOP_COST; } } bspace = (int *)Marshal.AllocHGlobal(nvtxs * sizeof(int)); weightsum = (double *)Marshal.AllocHGlobal(nsets * sizeof(double)); locked = (double *)Marshal.AllocHGlobal(nsets * sizeof(double)); loose = (double *)Marshal.AllocHGlobal(nsets * sizeof(double)); if (bspace == null || weightsum == null || locked == null || loose == null) { Marshal.FreeHGlobal((IntPtr)loose); Marshal.FreeHGlobal((IntPtr)locked); Marshal.FreeHGlobal((IntPtr)weightsum); Marshal.FreeHGlobal((IntPtr)bspace); return(true); } if (*bndy_list != null) { bdy_ptr = *bndy_list; list_length = 0; while (*bdy_ptr != 0) { bspace[list_length++] = *bdy_ptr++; } Marshal.FreeHGlobal((IntPtr)(*bndy_list)); if (list_length == 0) /* No boundary -> make everybody bndy. */ { for (i = 0; i < nvtxs; i++) { bspace[i] = i + 1; } list_length = nvtxs; } /* Set dvals to flag uninitialized vertices. */ for (i = 1; i <= nvtxs; i++) { dvals[i][0] = 3 * maxdval; } } else { list_length = nvtxs; } step_cutoff = KL_BAD_MOVES; cost_cutoff = maxdval * step_cutoff / 7; if (cost_cutoff < step_cutoff) { cost_cutoff = step_cutoff; } deltaminus = deltaplus = 0; for (i = 0; i < nsets; i++) { if (startweight[i] - goal[i] > deltaplus) { deltaplus = startweight[i] - goal[i]; } else if (goal[i] - startweight[i] > deltaminus) { deltaminus = goal[i] - startweight[i]; } } balanced = (deltaplus + deltaminus <= max_dev); bestg_min = -2.0 * nvtxs * maxdval; parity = false; eweight = (int)(cut_cost + .5); nbad = 0; npass = 0; improved = 0; done = false; while (!done) { npass++; ever_balanced = false; /* Initialize various quantities. */ balance_best = 0; for (i = 0; i < nsets; i++) { for (j = 0; j < nsets; j++) { tops[i][j] = 2 * maxdval; } weightsum[i] = startweight[i]; loose[i] = weightsum[i]; locked[i] = 0; balance_best += goal[i]; } gtotal = 0; bestg = bestg_min; beststep = -1; movelist = null; endlist = &movelist; neg_steps = 0; /* Compute the initial d-values, and bucket-sort them. */ time = seconds(); if (nsets == 2) { bucketsorts_bi(graph, nvtxs, buckets, listspace, dvals, sets, term_wgts, maxdval, nsets, parity, hops, bspace, list_length, npass, useEdgeWeights); } else { bucketsorts(graph, nvtxs, buckets, listspace, dvals, sets, term_wgts, maxdval, nsets, parity, hops, bspace, list_length, npass, useEdgeWeights); } parity = !parity; kl_bucket_time += seconds() - time; if (DEBUG_KL == DebugFlagKL.PrintBucket) { pbuckets(buckets, listspace, maxdval, nsets); } /* Now determine the set of K-L moves. */ for (step = 1;; step++) { /* Find the highest d-value in each set. */ /* But only consider moves from large to small sets, or moves */ /* in which balance is preserved. */ /* Break ties in some nonarbitrary manner. */ bestval = -maxdval - 1; for (i = 0; i < nsets; i++) { for (j = 0; j < nsets; j++) { /* Only allow moves from large sets to small sets, or */ /* moves which preserve balance. */ if (i != j) { /* Find the best move from i to j. */ for (k = tops[i][j]; k >= 0 && buckets[i][j][k] == null; k--) { ; } tops[i][j] = k; if (k >= 0) { l = (j > i) ? j - 1 : j; vtx = ((int)(buckets[i][j][k] - listspace[l])) / size; vweight = graph[vtx]->vwgt; if ((enforce_balance_hard && weightsum[i] >= goal[i] && weightsum[j] <= goal[j] && weightsum[i] - goal[i] - (weightsum[j] - goal[j]) > max_dev) || (!enforce_balance_hard && weightsum[i] >= goal[i] && weightsum[j] <= goal[j]) || (!enforce_balance_hard && weightsum[i] - vweight - goal[i] > -(double)((max_dev + 1) / 2) && weightsum[j] + vweight - goal[j] < (double)((max_dev + 1) / 2))) { /* Is it the best move seen so far? */ if (k - maxdval > bestval) { bestval = k - maxdval; bestvtx = vtx; bestto = j; /* DO I NEED ALL THIS DATA? Just to break ties. */ bestdelta = Math.Abs(weightsum[i] - vweight - goal[i]) + Math.Abs(weightsum[j] + vweight - goal[j]); beststuck1 = (int)Math.Min(loose[i], goal[j] - locked[j]); beststuck2 = (int)Math.Max(loose[i], goal[j] - locked[j]); } else if (k - maxdval == bestval) { /* Tied. Is better balanced than current best? */ /* If tied, move among sets with most freedom. */ stuck1st = (int)Math.Min(loose[i], goal[j] - locked[j]); stuck2nd = (int)Math.Max(loose[i], goal[j] - locked[j]); delta = Math.Abs(weightsum[i] - vweight - goal[i]) + Math.Abs(weightsum[j] + vweight - goal[j]); /* NOTE: Randomization in this check isn't ideal */ /* if more than two guys are tied. */ if (delta < bestdelta || (delta == bestdelta && (stuck1st > beststuck1 || (stuck1st == beststuck1 && (stuck2nd > beststuck2 || (stuck2nd == beststuck2 && (KL_RANDOM && drandom() < .5))))))) { bestval = k - maxdval; bestvtx = vtx; bestto = j; bestdelta = delta; beststuck1 = stuck1st; beststuck2 = stuck2nd; } } } } } } } if (bestval == -maxdval - 1) /* No allowed moves */ { if (DEBUG_KL != DebugFlagKL.NoDebugging) { Console.WriteLine("No KL moves at step {0:d}. bestg = {1:g} at step {2:d}.\n", step, bestg, beststep); } break; } bestptr = &(listspace[0][bestvtx]); bestfrom = sets[bestvtx]; vweight = graph[bestvtx]->vwgt; weightsum[bestto] += vweight; weightsum[bestfrom] -= vweight; loose[bestfrom] -= vweight; locked[bestto] += vweight; if (enforce_balance) /* Check if this partition is balanced. */ { deltaminus = deltaplus = 0; for (i = 0; i < nsets; i++) { if (weightsum[i] - goal[i] > deltaplus) { deltaplus = weightsum[i] - goal[i]; } else if (goal[i] - weightsum[i] > deltaminus) { deltaminus = goal[i] - weightsum[i]; } } balance_val = deltaminus + deltaplus; temp_balanced = (balance_val <= max_dev); ever_balanced = (ever_balanced || temp_balanced); } gtotal += bestval; if (((gtotal > bestg && (!enforce_balance || temp_balanced)) || (enforce_balance_hard && balance_val < balance_best)) && step != nvtxs) { bestg = gtotal; beststep = step; if (enforce_balance_hard) { balance_best = balance_val; } if (temp_balanced) { enforce_balance_hard = false; } } if (DEBUG_KL == DebugFlagKL.MoreInfo || DEBUG_KL == DebugFlagKL.PrintBucket) { Console.WriteLine("At KL step {0:d}, bestvtx={1:d}, bestval={2:d} ({3:d}-> {4:d})", step, bestvtx, bestval, bestfrom, bestto); } /* Monitor the stopping criteria. */ if (bestval < 0) { if (!enforce_balance || ever_balanced) { neg_steps++; } if (bestg != bestg_min) { neg_cost = (int)(bestg - gtotal); } else { neg_cost = -maxdval - 1; } if ((neg_steps > step_cutoff || neg_cost > cost_cutoff) && !(enforce_balance && bestg == bestg_min) && (beststep != step)) { if (DEBUG_KL != DebugFlagKL.NoDebugging) { if (neg_steps > step_cutoff) { Console.WriteLine("KL step cutoff at step {0:d}. bestg = {1:g} at step {2:d}.", step, bestg, beststep); } else if (neg_cost > cost_cutoff) { Console.WriteLine("KL cost cutoff at step {0:d}. bestg = {1:g} at step {2:d}.", step, bestg, beststep); } } break; } } else if (bestval > 0) { neg_steps = 0; } /* Remove vertex from its buckets, and flag it as finished. */ l = 0; for (k = 0; k < nsets; k++) { if (k != bestfrom) { dval = dvals[bestvtx][l] + maxdval; removebilist(&listspace[l][bestvtx], &buckets[bestfrom][k][dval]); l++; } } /* Is there a better way to do this? */ sets[bestvtx] = -sets[bestvtx] - 1; /* Set up the linked list of moved vertices. */ bestptr->next = null; bestptr->prev = (bilist *)(ulong)bestto; *endlist = bestptr; endlist = &(bestptr->next); /* Now update the d-values of all the neighbors */ edges = graph[bestvtx]->edges; if (useEdgeWeights) { ewptr = graph[bestvtx]->ewgts; } for (j = graph[bestvtx]->nedges - 1; j != 0; j--) { neighbor = *(++edges); if (useEdgeWeights) { eweight = (int)(*(++ewptr) * cut_cost + .5); } /* First make sure neighbor is alive. */ if (sets[neighbor] >= 0) { group = sets[neighbor]; if (dvals[neighbor][0] >= 3 * maxdval) { /* New vertex, not yet in buckets. */ /* Can't be neighbor of moved vtx, so compute */ /* initial dvals and buckets, then update. */ bucketsort1(graph, neighbor, buckets, listspace, dvals, sets, term_wgts, maxdval, nsets, hops, useEdgeWeights); } l = 0; for (k = 0; k < nsets; k++) { if (k != group) { diff = eweight * (hops[k][bestfrom] - hops[group][bestfrom] + hops[group][bestto] - hops[k][bestto]); dval = dvals[neighbor][l] + maxdval; movebilist(&listspace[l][neighbor], &buckets[group][k][dval], &buckets[group][k][dval + diff]); dvals[neighbor][l] += diff; dval += diff; if (dval > tops[group][k]) { tops[group][k] = dval; } l++; } } } } if (DEBUG_KL == DebugFlagKL.PrintBucket) { pbuckets(buckets, listspace, maxdval, nsets); } } /* Done with a pass; should we actually perform any swaps? */ bptr = movelist; if (bestg > 0 || (bestg != bestg_min && !balanced && enforce_balance) || (bestg != bestg_min && balance_trouble)) { improved += (int)bestg; for (i = 1; i <= beststep; i++) { vtx = ((int)(bptr - listspace[0])) / size; bestto = (int)(ulong)bptr->prev; startweight[bestto] += graph[vtx]->vwgt; startweight[-sets[vtx] - 1] -= graph[vtx]->vwgt; sets[vtx] = bestto; bptr = bptr->next; } deltaminus = deltaplus = 0; for (i = 0; i < nsets; i++) { if (startweight[i] - goal[i] > deltaplus) { deltaplus = startweight[i] - goal[i]; } else if (goal[i] - startweight[i] > deltaminus) { deltaminus = goal[i] - startweight[i]; } } /* * printf(" deltaplus = %f, deltaminus = %f, max_dev = %d\n", deltaplus, deltaminus, max_dev); */ balanced = (deltaplus + deltaminus <= max_dev); } else { nbad++; } if (!balanced || bptr == movelist) { if (enforce_balance) { if (enforce_balance_hard) { balance_trouble = true; } enforce_balance_hard = true; } enforce_balance = true; nbad++; } worth_undoing = (step < undo_frac * nvtxs); done = (nbad >= nbadtries && balanced); if (KL_MAX_PASS > 0) { done = done || (npass == KL_MAX_PASS && balanced); } if (!done) /* Prepare for next pass. */ { if (KL_UNDO_LIST && worth_undoing && !balance_trouble) { /* Make a list of modified vertices for next bucketsort. */ /* Also, ensure these vertices are removed from their buckets. */ list_length = make_kl_list(graph, movelist, buckets, listspace, sets, nsets, bspace, dvals, maxdval); } } if (done || !(KL_UNDO_LIST && worth_undoing && !balance_trouble)) { /* Restore set numbers of remaining, altered vertices. */ while (bptr != null) { vtx = ((int)(bptr - listspace[0])) / size; sets[vtx] = -sets[vtx] - 1; bptr = bptr->next; } list_length = nvtxs; } if (done && *bndy_list != null) { make_bndy_list(graph, movelist, buckets, listspace, sets, nsets, bspace, tops, bndy_list); } } if (DEBUG_KL != DebugFlagKL.NoDebugging) { Console.WriteLine(" KL required {0:d} passes to improve by {1:d}.", npass, improved); } Marshal.FreeHGlobal((IntPtr)loose); Marshal.FreeHGlobal((IntPtr)locked); Marshal.FreeHGlobal((IntPtr)weightsum); Marshal.FreeHGlobal((IntPtr)bspace); return(false); }