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2010•Unpublished venueRequires access

Finding the Maximum Matching in a Bipartite Graph

B. M. Monjurul Alom, Md. Saiful Islam

Open publisher page 5 citations

Abstract

A matching M of the graph G is an edge set such that no two edges of M share their endpoints. For a bipartite graph G = (V, E) maximum matching are matching whose cardinalities are maximum among all matchings. Existing enumerating algorithm of maximum matching has time complexity is O(|V |) per matching. FordFulkerson method finds the maximum matching on a bipartite graph with O(VE) time. In this paper, an algorithm to find the maximum matching on a bipartite graph with O(E) time is presented which is less than the time complexity of the existing algorithms.

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What this paper is about

A matching M of the graph G is an edge set such that no two edges of M share their endpoints. For a bipartite graph G = (V, E) maximum matching are matching whose cardinalities are maximum among all matchings. Existing enumerating algorithm of maximum matching has time complexity is O(|V |) per matching. FordFulkerson method finds the maximum matching on a bipartite graph with O(VE) time. In this paper, an algorithm to find the maximum matching on a bipartite graph with O(E) time is presented which is less than the time complexity of the existing algorithms.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A matching M of the graph G is an edge set such that no two edges of M share their endpoints. For a bipartite graph G = (V, E) maximum matching are matching whose cardinalities are maximum among all matchings. Existing enumerating algorithm of maximum matching has time complexity is O(|V |) per matching. FordFulkerson method finds the maximum matching on a bipartite graph with O(VE) time. In this paper, an algorithm to find the maximum matching on a bipartite graph with O(E) time is presented which is less than the time complexity of the existing algorithms.

Key concepts: Bipartite graph, 3-dimensional matching, Combinatorics, Matching (statistics), Factor-critical graph, Mathematics, Blossom algorithm, Complete bipartite graph

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