MaximumMatching.cs

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#region License
/*This file is part of Satsuma Graph Library
Copyright © 2013 Balázs Szalkai

This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.

Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:

   1. The origin of this software must not be misrepresented; you must not
   claim that you wrote the original software. If you use this software
   in a product, an acknowledgment in the product documentation would be
   appreciated but is not required.

   2. Altered source versions must be plainly marked as such, and must not be
   misrepresented as being the original software.

   3. This notice may not be removed or altered from any source
   distribution.*/
#endregion

using System;
using System.Collections.Generic;
using System.Linq;

namespace Satsuma
{
    public sealed class MaximumMatching : IClearable
    {
        public IGraph Graph { get; private set; }
        public Func<Node, bool> IsRed { get; private set; }

        private readonly Matching matching;

        public IMatching Matching { get { return matching; } }

        private readonly HashSet<Node> unmatchedRedNodes;

        public MaximumMatching(IGraph graph, Func<Node, bool> isRed)
        {
            Graph = graph;
            IsRed = isRed;
            matching = new Matching(Graph);
            unmatchedRedNodes = new HashSet<Node>();

            Clear();
        }

        public void Clear()
        {
            matching.Clear();
            unmatchedRedNodes.Clear();
            foreach (var n in Graph.Nodes())
                if (IsRed(n)) unmatchedRedNodes.Add(n);

        }

        public int GreedyGrow(int maxImprovements = int.MaxValue)
        {
            int result = 0;
            List<Node> matchedRedNodes = new List<Node>();
            foreach (var x in unmatchedRedNodes)
                    foreach (var arc in Graph.Arcs(x))
                    {
                        Node y = Graph.Other(arc, x);
                        if (!matching.HasNode(y))
                        {
                            matching.Enable(arc, true);
                            matchedRedNodes.Add(x);
                            result++;
                            if (result >= maxImprovements) goto BreakAll;
                            break;
                        }
                    }
        BreakAll:
            foreach (var n in matchedRedNodes) unmatchedRedNodes.Remove(n);
            return result;
        }

        public void Add(Arc arc)
        {
            if (matching.HasArc(arc)) return;
            matching.Enable(arc, true);
            Node u = Graph.U(arc);
            unmatchedRedNodes.Remove(IsRed(u) ? u : Graph.V(arc));
        }

        private Dictionary<Node, Arc> parentArc;
        private Node Traverse(Node node)
        {
            Arc matchedArc = matching.MatchedArc(node);

            if (IsRed(node))
            {
                foreach (var arc in Graph.Arcs(node))
                    if (arc != matchedArc)
                    {
                        Node y = Graph.Other(arc, node);
                        if (!parentArc.ContainsKey(y))
                        {
                            parentArc[y] = arc;
                            if (!matching.HasNode(y)) return y;
                            Node result = Traverse(y);
                            if (result != Node.Invalid) return result;
                        }
                    }
            }
            else
            {
                Node y = Graph.Other(matchedArc, node);
                if (!parentArc.ContainsKey(y))
                {
                    parentArc[y] = matchedArc;
                    Node result = Traverse(y);
                    if (result != Node.Invalid) return result;
                }
            }

            return Node.Invalid;
        }

        public void Run()
        {
            List<Node> matchedRedNodes = new List<Node>();
            parentArc = new Dictionary<Node, Arc>();
            foreach (var x in unmatchedRedNodes)
            {
                parentArc.Clear();
                parentArc[x] = Arc.Invalid;

                // find an alternating path
                Node y = Traverse(x);
                if (y == Node.Invalid) continue;

                // modify matching along the alternating path
                while (true)
                {
                    // y ----arc---- z (====arc2===)
                    Arc arc = parentArc[y];
                    Node z = Graph.Other(arc, y);
                    Arc arc2 = (z == x ? Arc.Invalid : parentArc[z]);
                    if (arc2 != Arc.Invalid) matching.Enable(arc2, false);
                    matching.Enable(arc, true);
                    if (arc2 == Arc.Invalid) break;
                    y = Graph.Other(arc2, z);
                }

                matchedRedNodes.Add(x);
            }
            parentArc = null;

            foreach (var n in matchedRedNodes) unmatchedRedNodes.Remove(n);
        }
    }
}