Date of Award
Department of Computer Science
We seek to compute perfect matchings of a d-regular bipartite multigraph G = (V, E). If d is a power of 2, we can perform Euler decomposition, which recursively separates a graph of even degree into subgraphs of smaller degree. When d is not a power of 2, however, Euler decomposition eventually returns a subgraph of odd degree. At this point, we can manually remove a perfect matching to return the graph to even degree and continue Euler decomposition. In this paper, we explore push-relabel algorithms as potential solutions to removing a perfect matching from a regular bipartite multigraph. Empirical analysis shows that these maximum-flow approaches, augmented by preflow-conditioning heuristics, find a perfect matching in O(E) time. Our experiments also suggest that the relabel-to-front algorithm is optimal for bipartite maximum-flow networks.
Coleman, Benjamin J., "Push-relabel algorithms for computing perfect matchings of regular bipartite multigraphs" (2020). Dartmouth College Undergraduate Theses. 154.