2011/05/08 by Bala Chandran, Dorit S. Hochbaum, Chandran, Bala G. +1
Chemistry · Computer Science · #Advanced Graph Theory Research #Asymmetric Hydrogenation and Catalysis #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Network Packet Processing and Optimization #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1105.1569
openalex publication_date 2011/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the pseudoflow algorithm for maximum flow is particularly\nefficient for the bipartite matching problem both in theory and in practice. We\ndevelop several implementations of the pseudoflow algorithm for bipartite\nmatching, and compare them over a wide set of benchmark instances to\nstate-of-the-art implementations of push-relabel and augmenting path algorithms\nthat are specifically designed to solve these problems. The experiments show\nthat the pseudoflow variants are in most cases faster than the other\nalgorithms.\n We also show that one particular implementation---the matching pseudoflow\nalgorithm---is theoretically efficient. For a graph with n nodes, m arcs,\nn1 the size of the smaller set in the bipartition, and the maximum matching\nvalue \κ \≤ n1, the algorithm's complexity given input in the form of\nadjacency lists is O(\minn1\κ,m + \√(\κ)\min\κ2,m).\nSimilar algorithmic ideas are shown to work for an adaptation of Hopcroft and\nKarp's bipartite matching algorithm with the same complexity. Using boolean\noperations on words of size \λ, the complexity of the pseudoflow\nalgorithm is further improved to O(\minn1\κ, \(n1n2)/(\λ), m\n+ \κ2 + frac\κ2.5\λ). This run time is faster than for\nprevious algorithms such as Cheriyan and Mehlhorn's algorithm of complexity\nO( fracn2.5\λ).\n