A matching algorithms based on the depth first search for the general graph

Abstract

In this paper, a matching algorithm of general graph based on depth-first traversal is proposed. The algorithm does not need to shrink and expand treatment when a flower is searched. This algorithm's time complexity of search an augmenting path is equal to corresponding graph's depth-first traversal algorithm's time complexity, it is one of the most efficient algorithm. Experiments show that this algorithm can correctly handle the associated practical problems, and have the correct conclusion. The research on the matching theories and the matching algorithms are one of the core content in the area of graph theory and application research. It has a strong application background. The research results are widely used in process arrangement, personnel assignment, information transfer, and transportation problem etc. The algorithm about matching problem is proposed first by Kuhn (1) and Hall (2) for search the perfect matching in a bipartite graph, it is a linear programming algorithm. In 1965, the flower algorithm is proposed by Edmonds to look for the perfect matching in a non-bipartite graph, it is a effective algorithm (3, 4). The better implementation algorithms (5, 6), the effective implementation algorithm of Edmonds method is proposed by Gabow (7). Some other effective label method similar to Gabow algorithm (8, 9, 10), the algorithm's time complexity to . In this paper, a matching algorithm of general graph based on depth-first traversal is proposed. The algorithm does not need to shrink and expand treatment when a flower is searched.