# 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 11/7-approximation for the T-tour problem and show that the integrality ratio of the standard LP relaxation is at most 11/7. 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]).

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