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#include <stdio.h>
#include "PerfectMatching.h"
#include "LCA.h"
struct Node
{
PerfectMatching::REAL sum; // = twice_y[i] + twice_y[i->parent] + twice_y[i->parent->parent] + ...
Node* match;
Node* parent;
Node* child;
Node* sibling;
int lca_preorder;
};
int CheckPerfectMatchingOptimality(int node_num, int edge_num, int* edges, int* weights, PerfectMatching* pm, PerfectMatching::REAL threshold)
{
int _i, _j, _e;
Node* i;
Node* j;
int blossom_num = pm->GetBlossomNum();
int* blossom_parents = new int[node_num+blossom_num];
PerfectMatching::REAL* twice_y = new PerfectMatching::REAL[node_num+blossom_num];
PerfectMatching::REAL y_blossom_min = 0;
PerfectMatching::REAL slack_min = 0;
PerfectMatching::REAL active_slack_max = 0;
// step 1 - read dual solution and construct tree
pm->GetDualSolution(blossom_parents, twice_y);
Node* nodes = new Node[node_num+blossom_num+1];
memset(nodes, 0, (node_num+blossom_num+1)*sizeof(Node));
Node* ROOT = nodes+node_num+blossom_num;
for (_i=0, i=nodes; _i<node_num+blossom_num; _i++, i++)
{
i->sum = twice_y[_i];
if (_i >= node_num && y_blossom_min > i->sum) y_blossom_min = i->sum;
if (blossom_parents[_i] >= 0)
{
if (blossom_parents[_i]<node_num || blossom_parents[_i]>=node_num+blossom_num)
{
delete [] nodes;
delete [] blossom_parents;
delete [] twice_y;
return 2;
}
i->parent = nodes + blossom_parents[_i];
i->sibling = i->parent->child;
i->parent->child = i;
}
}
delete [] blossom_parents;
delete [] twice_y;
for (i=nodes; i<nodes+node_num+blossom_num; i++)
{
if (!i->parent)
{
i->parent = ROOT;
i->sibling = ROOT->child;
ROOT->child = i;
}
}
LCATree* lca_tree = new LCATree(node_num+blossom_num+1);
Node** rev_mapping = new Node*[node_num+blossom_num];
i = ROOT;
while ( 1 )
{
if (i->child)
{
if (i < nodes+node_num) { delete [] nodes; delete lca_tree; delete [] rev_mapping; return 2; }
i->child->sum += i->sum;
i = i->child;
}
else
{
if (i >= nodes+node_num) { delete [] nodes; delete lca_tree; delete [] rev_mapping; return 2; }
while ( 1 )
{
i->lca_preorder = lca_tree->Add(i, i->parent);
rev_mapping[i->lca_preorder] = i;
if (i->sibling) break;
i = i->parent;
if (i == ROOT)
{
i->lca_preorder = lca_tree->AddRoot(i);
break;
}
}
if (i == ROOT) break;
i = i->sibling;
i->sum += i->parent->sum;
}
}
int matched_num = 0;
for (_e=0; _e<edge_num; _e++)
{
_i = edges[2*_e];
_j = edges[2*_e+1];
if (_i<0 || _j<0 || _i>=node_num || _j>=node_num || _i==_j) { delete [] nodes; delete lca_tree; delete [] rev_mapping; return 2; }
int lca_i = nodes[_i].lca_preorder;
int lca_j = nodes[_j].lca_preorder;
lca_tree->GetPenultimateNodes(lca_i, lca_j);
i = rev_mapping[lca_i];
j = rev_mapping[lca_j];
PerfectMatching::REAL twice_slack = 2*weights[_e] - (nodes[_i].sum - i->parent->sum) - (nodes[_j].sum - j->parent->sum);
if (slack_min > twice_slack) slack_min = twice_slack;
if (pm->GetSolution(_e))
{
if (pm->GetMatch(_i)!=_j || pm->GetMatch(_j)!=_i || i->match || j->match) { delete [] nodes; delete lca_tree; delete [] rev_mapping; return 2; }
i->match = j;
j->match = i;
if (active_slack_max < twice_slack) active_slack_max = twice_slack;
matched_num += 2;
}
}
delete [] nodes;
delete lca_tree;
delete [] rev_mapping;
if (matched_num != node_num) return 2;
if (y_blossom_min < -threshold || slack_min < -threshold || active_slack_max > threshold)
{
printf("ERROR in CheckPerfectMatchingOptimality():\n");
if ( ((PerfectMatching::REAL)1 / 2) == 0 )
printf("\ty_blossom_min=%d\n\tslack_min=%d\n\tactive_slack_max=%d\n", (int)y_blossom_min, (int)slack_min, (int)active_slack_max);
else
printf("\ty_blossom_min=%.15f\n\tslack_min=%.15f\n\tactive_slack_max=%.15f\n", (double)y_blossom_min, (double)slack_min, (double)active_slack_max);
return 1;
}
return 0;
}
double ComputePerfectMatchingCost(int node_num, int edge_num, int* edges, int* weights, PerfectMatching* pm)
{
int i;
int j;
int e;
double cost = 0;
int* nodes = new int[node_num];
memset(nodes, 0, node_num*sizeof(int));
for (e=0; e<edge_num; e++)
{
if (pm->GetSolution(e))
{
i = edges[2*e];
j = edges[2*e+1];
nodes[i] ++;
nodes[j] ++;
cost += weights[e];
}
}
for (i=0; i<node_num; i++)
{
if (nodes[i] != 1)
{
printf("ComputeCost(): degree = %d!\n", nodes[i]);
exit(1);
}
}
delete [] nodes;
return cost;
}
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