1 files changed, 161 insertions, 0 deletions
diff --git a/src/backend/lib/bipartite_match.c b/src/backend/lib/bipartite_match.c
new file mode 100644
index 00000000000..57d6d548cff
--- /dev/null
+++ b/src/backend/lib/bipartite_match.c
@@ -0,0 +1,161 @@
+/*-------------------------------------------------------------------------
+ *
+ * bipartite_match.c
+ *	  Hopcroft-Karp maximum cardinality algorithm for bipartite graphs
+ *
+ * This implementation is based on pseudocode found at:
+ *
+ * http://en.wikipedia.org/w/index.php?title=Hopcroft%E2%80%93Karp_algorithm&oldid=593898016
+ *
+ * Copyright (c) 2015, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ *	  src/backend/lib/bipartite_match.c
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include <math.h>
+#include <limits.h>
+
+#include "lib/bipartite_match.h"
+#include "miscadmin.h"
+#include "utils/palloc.h"
+
+static bool hk_breadth_search(BipartiteMatchState *state);
+static bool hk_depth_search(BipartiteMatchState *state, int u, int depth);
+
+/*
+ * Given the size of U and V, where each is indexed 1..size, and an adjacency
+ * list, perform the matching and return the resulting state.
+ */
+BipartiteMatchState *
+BipartiteMatch(int u_size, int v_size, short **adjacency)
+{
+	BipartiteMatchState *state = palloc(sizeof(BipartiteMatchState));
+
+	Assert(u_size < SHRT_MAX);
+	Assert(v_size < SHRT_MAX);
+
+	state->u_size = u_size;
+	state->v_size = v_size;
+	state->matching = 0;
+	state->adjacency = adjacency;
+	state->pair_uv = palloc0((u_size + 1) * sizeof(short));
+	state->pair_vu = palloc0((v_size + 1) * sizeof(short));
+	state->distance = palloc((u_size + 1) * sizeof(float));
+	state->queue = palloc((u_size + 2) * sizeof(short));
+
+	while (hk_breadth_search(state))
+	{
+		int		u;
+
+		for (u = 1; u <= u_size; ++u)
+			if (state->pair_uv[u] == 0)
+				if (hk_depth_search(state, u, 1))
+					state->matching++;
+
+		CHECK_FOR_INTERRUPTS();		/* just in case */
+	}
+
+	return state;
+}
+
+/*
+ * Free a state returned by BipartiteMatch, except for the original adjacency
+ * list, which is owned by the caller. This only frees memory, so it's optional.
+ */
+void
+BipartiteMatchFree(BipartiteMatchState *state)
+{
+	/* adjacency matrix is treated as owned by the caller */
+	pfree(state->pair_uv);
+	pfree(state->pair_vu);
+	pfree(state->distance);
+	pfree(state->queue);
+	pfree(state);
+}
+
+static bool
+hk_breadth_search(BipartiteMatchState *state)
+{
+	int			usize = state->u_size;
+	short	   *queue = state->queue;
+	float	   *distance = state->distance;
+	int			qhead = 0;		/* we never enqueue any node more than once */
+	int			qtail = 0;		/* so don't have to worry about wrapping */
+	int			u;
+
+	distance[0] = INFINITY;
+
+	for (u = 1; u <= usize; ++u)
+	{
+		if (state->pair_uv[u] == 0)
+		{
+			distance[u] = 0;
+			queue[qhead++] = u;
+		}
+		else
+			distance[u] = INFINITY;
+	}
+
+	while (qtail < qhead)
+	{
+		u = queue[qtail++];
+
+		if (distance[u] < distance[0])
+		{
+			short  *u_adj = state->adjacency[u];
+			int		i = u_adj ? u_adj[0] : 0;
+
+			for (; i > 0; --i)
+			{
+				int	u_next = state->pair_vu[u_adj[i]];
+
+				if (isinf(distance[u_next]))
+				{
+					distance[u_next] = 1 + distance[u];
+					queue[qhead++] = u_next;
+					Assert(qhead <= usize+2);
+				}
+			}
+		}
+	}
+
+	return !isinf(distance[0]);
+}
+
+static bool
+hk_depth_search(BipartiteMatchState *state, int u, int depth)
+{
+	float	   *distance = state->distance;
+	short	   *pair_uv = state->pair_uv;
+	short	   *pair_vu = state->pair_vu;
+	short	   *u_adj = state->adjacency[u];
+	int			i = u_adj ? u_adj[0] : 0;
+
+	if (u == 0)
+		return true;
+
+	if ((depth % 8) == 0)
+		check_stack_depth();
+
+	for (; i > 0; --i)
+	{
+		int		v = u_adj[i];
+
+		if (distance[pair_vu[v]] == distance[u] + 1)
+		{
+			if (hk_depth_search(state, pair_vu[v], depth+1))
+			{
+				pair_vu[v] = u;
+				pair_uv[u] = v;
+				return true;
+			}
+		}
+	}
+
+	distance[u] = INFINITY;
+	return false;
+}