An Improved Approximation Algorithm for Maximum Weight 3-Path Packing

Abstract

Given a complete graph with $n$ vertices and non-negative edge weights, where $n$ is divisible by 3, the maximum weight 3-path packing problem is to find a set of $n/3$ vertex-disjoint 3-paths such that the total weight of the 3-paths in the packing is maximized. This problem is closely related to the classic maximum weight matching problem. In this paper, we propose a $10/17$-approximation algorithm, improving the best-known $7/12$-approximation algorithm (ESA 2015). Our result is obtained by making a trade-off among three algorithms. The first is based on the maximum weight matching of size