Fast and Simple Algorithms for Weighted Perfect Matching

Abstract

We present two fast and simple combinatorial approximation algorithms for constructing a minimum-weighted perfect matching on complete graphs whose cost functions satisfy the triangle inequality. The rst algorithm runs in O(n 2 logn) time and is at most a factor logn worse than an optimal solution. In the second algorithm, the average time until a node is matched is O(n 2 ) and the approximation ratio is log 2 n.