From fcca22a2f05b582d0d9bc87eaf529275e141bef9 Mon Sep 17 00:00:00 2001
From: eugenefischer <66030419+eugenefischer@users.noreply.github.com>
Date: Sat, 22 Oct 2022 13:18:43 -0500
Subject: [PATCH] Rename class, modify bidding to include marginal item value

---
 ...IntegerWeightBipartiteAuctionMatching.java | 157 ++++++++++++++++++
 1 file changed, 157 insertions(+)
 create mode 100644 src/main/java/MaximumIntegerWeightBipartiteAuctionMatching.java

diff --git a/src/main/java/MaximumIntegerWeightBipartiteAuctionMatching.java b/src/main/java/MaximumIntegerWeightBipartiteAuctionMatching.java
new file mode 100644
index 0000000..aee42e1
--- /dev/null
+++ b/src/main/java/MaximumIntegerWeightBipartiteAuctionMatching.java
@@ -0,0 +1,157 @@
+import org.jgrapht.Graph;
+import org.jgrapht.GraphTests;
+import org.jgrapht.alg.interfaces.MatchingAlgorithm;
+
+import java.math.BigDecimal;
+import java.util.*;
+
+/*
+Maximum weight matching in bipartite graphs using a forward auction algorithm. This implementation uses the Gauss-Seidel
+version of the forward auction algorithm, in which bids are submitted one at a time. For any weighted bipartite graph
+with n vertices in the smaller partition, this algorithm will produce a matching that is within n*epsilon of being
+optimal. For a weighted bipartite graph with strictly integer weights, this matching will always be optimal, and thus
+is a maximum weight matching.
+ */
+
+public class MaximumIntegerWeightBipartiteAuctionMatching<V, E> implements MatchingAlgorithm<V, E> {
+
+    private final Graph<V, E> graph;
+    private final Set<V> partition1;
+    private final Set<V> partition2;
+    private final BigDecimal epsilon;
+    private final Set<E> matching;
+    private BigDecimal matchingWeight;
+    private boolean swappedPartitions = false;
+
+    public MaximumIntegerWeightBipartiteAuctionMatching(Graph<V, E> graph, Set<V> partition1, Set<V> partition2) {
+        this.graph = GraphTests.requireUndirected(graph);
+        this.partition1 = Objects.requireNonNull(partition1, "Partition 1 cannot be null");
+        this.partition2 = Objects.requireNonNull(partition2, "Partition 2 cannot be null");
+        int n = Math.max(partition1.size(), partition2.size());
+        this.epsilon = BigDecimal.valueOf(1 / ((double) n + 1));
+        this.matching = new LinkedHashSet<>();
+        this.matchingWeight = BigDecimal.ZERO;
+    }
+
+
+    /*
+    Method coded using MaximumWeightBipartiteMatching.class from JgraphT as a model
+     */
+    @Override
+    public Matching<V, E> getMatching() {
+
+        /*
+         * Test input instance
+         */
+        if (!GraphTests.isSimple(graph)) {
+            throw new IllegalArgumentException("Only simple graphs supported");
+        }
+        if (!GraphTests.isBipartitePartition(graph, partition1, partition2)) {
+            throw new IllegalArgumentException("Graph partition is not bipartite");
+        }
+
+        /*
+        If the two partitions are different sizes, the bidders must be the smaller of the two partitions.
+         */
+        Set<V> items;
+        Set<V> bidders;
+        if (partition2.size() >= partition1.size()) {
+            bidders = partition1;
+            items = partition2;
+        }
+        else {
+            bidders = partition2;
+            items = partition1;
+            swappedPartitions = true;
+        }
+
+        /*
+        Create a map to track the owner of each item, which is initially null,
+        and a map to track the price of each item, which is initially 0.
+         */
+        Map<V, V> owners = new HashMap<>();
+        Map<V, BigDecimal> prices = new HashMap<>();
+        for(V item: items) {
+            owners.put(item, null);
+            prices.put(item, BigDecimal.ZERO);
+        }
+
+        //Initialize queue of all bidders that don't currently own an item
+        Queue<V> unmatchedBidders = new ArrayDeque<>();
+        for(V bidder: bidders) {
+            unmatchedBidders.offer(bidder);
+        }
+
+        while (unmatchedBidders.size() > 0) {
+            V bidder = unmatchedBidders.poll();
+            V item = null;
+            BigDecimal bestValue = BigDecimal.valueOf(-1.0);
+            BigDecimal runnerUpValue = BigDecimal.valueOf(-1.0);
+            /*
+            Find the items that offer the best and second-best value for the bidder,
+            then submit a bid equal to the price of the best item plus the marginal value over
+            the second-best item plus delta.
+             */
+            for (E edge: graph.edgesOf(bidder)) {
+                double weight = graph.getEdgeWeight(edge);
+                if(weight == 0.0) {
+                    continue;
+                }
+                V tmp = getItem(bidder, edge);
+                BigDecimal value = BigDecimal.valueOf(weight).subtract(prices.get(tmp));
+                if (value.compareTo(bestValue) >= 0) {
+                    runnerUpValue = bestValue;
+                    bestValue = value;
+                    item = tmp;
+                }
+                else if (value.compareTo(runnerUpValue) >= 0) {
+                    runnerUpValue = value;
+                }
+            }
+            if(bestValue.compareTo(BigDecimal.ZERO) >= 0) {
+                V formerOwner = owners.get(item);
+                BigDecimal price = prices.get(item);
+                BigDecimal bid = price.add(bestValue).subtract(runnerUpValue).add(epsilon);
+                if (formerOwner != null) {
+                    unmatchedBidders.offer(formerOwner);
+                }
+                owners.put(item, bidder);
+                prices.put(item, bid);
+            }
+        }
+        for (V item: owners.keySet()) {
+            if (owners.get(item) != null) {
+                matching.add(graph.getEdge(item, owners.get(item)));
+            }
+        }
+
+        for(E edge: matching) {
+            this.matchingWeight = this.matchingWeight.add(BigDecimal.valueOf(graph.getEdgeWeight(edge)));
+        }
+
+
+        return new MatchingImpl<>(graph, matching, matchingWeight.doubleValue());
+    }
+
+    private V getItem(V bidder, E edge) {
+        if (swappedPartitions) {
+            return graph.getEdgeSource(edge);
+        }
+        else {
+            return graph.getEdgeTarget(edge);
+        }
+    }
+
+    private V getBidder(V item, E edge) {
+        if (swappedPartitions) {
+            return graph.getEdgeTarget(edge);
+        }
+        else {
+            return graph.getEdgeSource(edge);
+        }
+    }
+
+    public BigDecimal getMatchingWeight() {
+        return matchingWeight;
+    }
+}