Improving on Best-of-Many-Christofides for [formula omitted]-tours

Abstract

The T-tour problem is a natural generalization of TSP and Path TSP. Given a graph G=(V,E), edge cost c:E→R≥0, and an even cardinality set T⊆V, we want to compute a minimum-cost T-join connecting all vertices of G (and possibly containing parallel edges).In this paper we give an 117-approximation for the T-tour problem and show that the integrality ratio of the standard LP relaxation is at most 117. Despite much progress for the special case Path TSP, for general T-tours this is the first improvement on Sebő’s analysis of the Best-of-Many-Christofides algorithm (Sebő, 2013).