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/*
* bipartite_match.h
*
* Copyright (c) 2015-2023, PostgreSQL Global Development Group
*
* src/include/lib/bipartite_match.h
*/
#ifndef BIPARTITE_MATCH_H
#define BIPARTITE_MATCH_H
/*
* Given a bipartite graph consisting of nodes U numbered 1..nU, nodes V
* numbered 1..nV, and an adjacency map of undirected edges in the form
* adjacency[u] = [k, v1, v2, v3, ... vk], we wish to find a "maximum
* cardinality matching", which is defined as follows: a matching is a subset
* of the original edges such that no node has more than one edge, and a
* matching has maximum cardinality if there exists no other matching with a
* greater number of edges.
*
* This matching has various applications in graph theory, but the motivating
* example here is Dilworth's theorem: a partially-ordered set can be divided
* into the minimum number of chains (i.e. subsets X where x1 < x2 < x3 ...) by
* a bipartite graph construction. This gives us a polynomial-time solution to
* the problem of planning a collection of grouping sets with the provably
* minimal number of sort operations.
*/
typedef struct BipartiteMatchState
{
/* inputs: */
int u_size; /* size of U */
int v_size; /* size of V */
short **adjacency; /* adjacency[u] = [k, v1,v2,v3,...,vk] */
/* outputs: */
int matching; /* number of edges in matching */
short *pair_uv; /* pair_uv[u] -> v */
short *pair_vu; /* pair_vu[v] -> u */
/* private state for matching algorithm: */
short *distance; /* distance[u] */
short *queue; /* queue storage for breadth search */
} BipartiteMatchState;
extern BipartiteMatchState *BipartiteMatch(int u_size, int v_size, short **adjacency);
extern void BipartiteMatchFree(BipartiteMatchState *state);
#endif /* BIPARTITE_MATCH_H */
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