Improving on Best-of-Many-Christofides for T-tours

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 [Formula presented]-approximation for the T-tour problem and show that the integrality ratio of the standard LP relaxation is at most [Formula presented]. 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). © 2020 ElsevierISSN:0167-6377ISSN:1872-746