An improved constant-time approximation algorithm for maximum~matchings

This paper studies constant-time approximation algorithms for problems on degree-bounded graphs. Let n and d be the number of vertices and the degree bound, respectively. This paper presents an algorithm that decides whether a vertex is contained in a some fixed maximal independent set with expected query complexity O(d2 ). Using this algorithm, it also shows that there are approximation algorithms with additive error n for many other problems, e.g., the maximum matching problem, the minimum vertex cover problem, and the minimum set cover problem, that run exponentially faster than existing algorithms with respect to d and 1 . Its approximation algorithm for the maximum matching can be transformed to a testing algorithm for the property of having a perfect matching with two-sided error. On the contrary, it also shows that every one-sided error tester for the property requires at least (n) queries.

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Yuichi Yoshida, Masaki Yamamoto, Hiro Ito
• Keywords: Algorithms, Approximation Algorithm, Maximum Matching Problem, STOC 2009, Vertex Cover Problem