Class: GraphMatching::Algorithm::MCMBipartite

Inherits:
MatchingAlgorithm show all
Defined in:
lib/graph_matching/algorithm/mcm_bipartite.rb

Overview

‘MCMBipartite` implements Maximum Cardinality Matching in bipartite graphs.

Direct Known Subclasses

MWMBipartite

Instance Attribute Summary

Attributes inherited from MatchingAlgorithm

#g

Instance Method Summary collapse

Methods inherited from MatchingAlgorithm

#assert

Constructor Details

#initialize(graph) ⇒ MCMBipartite

Returns a new instance of MCMBipartite.



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# File 'lib/graph_matching/algorithm/mcm_bipartite.rb', line 11

def initialize(graph)
  assert(graph).is_a(Graph::Bigraph)
  super
end

Instance Method Details

#match ⇒ Object 



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# File 'lib/graph_matching/algorithm/mcm_bipartite.rb', line 16

def match
  u = g.partition[0]
  m = []

  loop do
    # Begin each stage by clearing all labels and marks
    t = []
    predecessors = {}
    aug_path = nil

    # Label unmatched vertexes in U with label R.
    r = u.select { |i| m[i] == nil }

    # These R-vertexes are candidates for the start of an augmenting path.
    unmarked = r.dup.to_a

    # While there are unmarked R-vertexes
    loop do
      break unless aug_path.nil?
      start = unmarked.pop
      break unless start

      # Follow the unmatched edges (if any) to vertexes in V
      # ignoring any V-vertexes already labeled T
      unlabeled_across_unmatched_edges_from(start, g, m, t).each do |vi|
        t << vi
        predecessors[vi] = start

        # If there are matched edges, follow each to a vertex
        # in U and label the U-vertex with R.  Otherwise,
        # backtrack to construct an augmenting path.
        adj_u_in_m = matched_adjacent(vi, start, g, m)

        adj_u_in_m.each do |ui|
          r << ui
          unmarked << ui
          predecessors[ui] = vi
        end

        if adj_u_in_m.empty?
          aug_path = backtrack_from(vi, predecessors)
          break
        end
      end
    end

    if aug_path.nil?
      break
    else
      m = augment(m, aug_path)
    end
  end

  Matching.gabow(m)
end