2011/05/08 by Bala Chandran, Bala G. Chandran, Dorit S. Hochbaum +2
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 #cs.DS #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1105.1569
openalex publication_date 2011/05/08 · arxiv created 2011/05/09 · arxiv updated 2011/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the pseudoflow algorithm for maximum flow is particularly efficient for the bipartite matching problem both in theory and in practice. We develop several implementations of the pseudoflow algorithm for bipartite matching, and compare them over a wide set of benchmark instances to state-of-the-art implementations of push-relabel and augmenting path algorithms that are specifically designed to solve these problems. The experiments show that the pseudoflow variants are in most cases faster than the other algorithms. We also show that one particular implementation---the matching pseudoflow algorithm---is theoretically efficient. For a graph with n nodes, m arcs, n1 the size of the smaller set in the bipartition, and the maximum matching value κ≤ n1, the algorithm's complexity given input in the form of adjacency lists is O(minn1κ,m + √κminκ2,m). Similar algorithmic ideas are shown to work for an adaptation of Hopcroft and Karp's bipartite matching algorithm with the same complexity. Using boolean operations on words of size λ, the complexity of the pseudoflow algorithm is further improved to O(minn1κ, \fracn1n2λ, m + κ2 + \fracκ2.5λ). This run time is faster than for previous algorithms such as Cheriyan and Mehlhorn's algorithm of complexity O(\fracn2.5λ).