bipartite_match.c

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/*-------------------------------------------------------------------------
 *
 * bipartite_match.c
 *    Hopcroft-Karp maximum cardinality algorithm for bipartite graphs
 *
 * This implementation is based on pseudocode found at:
 *
 * https://en.wikipedia.org/w/index.php?title=Hopcroft%E2%80%93Karp_algorithm&oldid=593898016
 *
 * Copyright (c) 2015-2021, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/lib/bipartite_match.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <limits.h>

#include "lib/bipartite_match.h"
#include "miscadmin.h"

/*
 * The distances computed in hk_breadth_search can easily be seen to never
 * exceed u_size.  Since we restrict u_size to be less than SHRT_MAX, we
 * can therefore use SHRT_MAX as the "infinity" distance needed as a marker.
 */
#define HK_INFINITY  SHRT_MAX

static bool hk_breadth_search(BipartiteMatchState *state);
static bool hk_depth_search(BipartiteMatchState *state, int u);

/*
 * 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));

    if (u_size < 0 || u_size >= SHRT_MAX ||
        v_size < 0 || v_size >= SHRT_MAX)
        elog(ERROR, "invalid set size for BipartiteMatch");

    state->u_size = u_size;
    state->v_size = v_size;
    state->adjacency = adjacency;
    state->matching = 0;
    state->pair_uv = (short *) palloc0((u_size + 1) * sizeof(short));
    state->pair_vu = (short *) palloc0((v_size + 1) * sizeof(short));
    state->distance = (short *) palloc((u_size + 1) * sizeof(short));
    state->queue = (short *) 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))
                    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);
}

/*
 * Perform the breadth-first search step of H-K matching.
 * Returns true if successful.
 */
static bool
hk_breadth_search(BipartiteMatchState *state)
{
    int         usize = state->u_size;
    short      *queue = state->queue;
    short      *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] = HK_INFINITY;

    for (u = 1; u <= usize; u++)
    {
        if (state->pair_uv[u] == 0)
        {
            distance[u] = 0;
            queue[qhead++] = u;
        }
        else
            distance[u] = HK_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 (distance[u_next] == HK_INFINITY)
                {
                    distance[u_next] = 1 + distance[u];
                    Assert(qhead < usize + 2);
                    queue[qhead++] = u_next;
                }
            }
        }
    }

    return (distance[0] != HK_INFINITY);
}

/*
 * Perform the depth-first search step of H-K matching.
 * Returns true if successful.
 */
static bool
hk_depth_search(BipartiteMatchState *state, int u)
{
    short      *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;
    short       nextdist;

    if (u == 0)
        return true;
    if (distance[u] == HK_INFINITY)
        return false;
    nextdist = distance[u] + 1;

    check_stack_depth();

    for (; i > 0; i--)
    {
        int         v = u_adj[i];

        if (distance[pair_vu[v]] == nextdist)
        {
            if (hk_depth_search(state, pair_vu[v]))
            {
                pair_vu[v] = u;
                pair_uv[u] = v;
                return true;
            }
        }
    }

    distance[u] = HK_INFINITY;
    return false;
}