The Power of Linear-Time Data Reduction for Maximum Matching

Mertzios, G.B.; Nichterlein, A.; Niedermeier, R.

Abstract

Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in O(m\sqrt{n}) time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on linear-time kernelization. We start a deeper and systematic study both for general graphs and for bipartite graphs. Our data reduction algorithms easily comply (in form of preprocessing) with every solution strategy (exact, approximate, heuristic), thus making them attractive in various settings.

Citation

Mertzios, G., Nichterlein, A., & Niedermeier, R. (2017, August). The Power of Linear-Time Data Reduction for Maximum Matching. Presented at 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS)., Aalborg, Denmark

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS).
• Start Date: Aug 21, 2017
• End Date: Aug 25, 2017
• Acceptance Date: Jun 12, 2017
• Online Publication Date: Nov 1, 2017
• Publication Date: Dec 1, 2017
• Deposit Date: Jun 26, 2017
• Publicly Available Date: Jun 28, 2017
• Series Title: LIPIcs–Leibniz International Proceedings in Informatics
• Series Number: 83
• Series ISSN: 1868-8969
• Book Title: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) : August 21-25, 2017, Aalborg (Denmark) ; proceedings.
• DOI: https://doi.org/10.4230/lipics.mfcs.2017.46
• Public URL: https://durham-repository.worktribe.com/output/1146058