Tight Approximation Ratio for Minimum Maximal Matching

Szymon Dudycz; Mateusz Lewandowski; Jan Marcinkowski

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arXiv · 1811.08506

Tight Approximation Ratio for Minimum Maximal Matching

Szymon Dudycz·Mateusz Lewandowski·Jan Marcinkowski

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Abstract

We study a combinatorial problem called Minimum Maximal Matching, where we are asked to find in a general graph the smallest 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 $\frac{4}{3}$, 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 $\frac{3}{2}$.

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Szymon Dudycz, Mateusz Lewandowski, Jan Marcinkowski. 2018-11-20. Tight Approximation Ratio for Minimum Maximal Matching. https://arxiv.org/abs/1811.08506

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