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

2020/09/21 by Vera Traub, Traub, Vera
Computer Science · #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #cs.DM #cs.DS

paper · pdf · doi:10.48550/arxiv.2009.09743

arxiv created 2020/09/21 · arxiv updated 2020/09/22

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 (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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