We study a combinatorial problem called Minimum Maximal Matching, where we are asked to find in a general graph the smallest matching that can not be extended. We show that this problem is hard to approximate with a constant smaller than 2, assuming the Unique Games Conjecture. As a corollary we show, that Minimum Maximal Matching in bipartite graphs is hard to approximate with constant smaller than with the same assumption. With a stronger variant of the Unique Games Conjecture—that is Small Set Expansion Hypothesis—we are able to improve the hardness result up to the factor of.
CITATION STYLE
Dudycz, S., Lewandowski, M., & Marcinkowski, J. (2019). Tight Approximation Ratio for Minimum Maximal Matching. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11480 LNCS, pp. 181–193). Springer Verlag. https://doi.org/10.1007/978-3-030-17953-3_14
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