Abstract
Haxell's condition is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perfect matching in the bipartite hypergraph. Unlike in graphs, however, there is no known polynomial time algorithm to find the hypergraph perfect matching that is guaranteed to exist when Haxell's condition is satisfied. We prove the existence of an efficient algorithm to find perfect matchings in bipartite hypergraphs whenever a stronger version of Haxell's condition holds. Our algorithm can be seen as a generalization of the classical Hungarian algorithm for finding perfect matchings in bipartite graphs. The techniques we use to achieve this result could be of use more generally in other combinatorial problems on hypergraphs where disjointness structure is crucial, e.g. Set Packing.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
