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db_include/lib/bipartite_match.h

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+/*
+ * bipartite_match.h
+ *
+ * Copyright (c) 2015-2021, 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 */