Tight Inapproximability of Minimum Maximal Matching on Bipartite Graphs and Related Problems.

We study the Minimum Maximal Matching problem, where we are asked to find in a graph the smallest matching that cannot be extended. We show that this problem is hard to approximate with any constant smaller than 2 even in bipartite graphs, assuming either of two stronger variants of Unique Games Conjecture. The bound also holds for computationally equivalent Minimum Edge Dominating Set . Our lower bound matches the approximation provided by a trivial algorithm. Our results imply conditional hardness of approximating Maximum Stable Matching with Ties and Incomplete Lists with a constant better than 3 2 , which also matches the best known approximation algorithm.