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An Improved Analysis of the Mömke--Svensson Algorithm for Graph-TSP on Subquartic Graphs (Journal Version)

Alantha Newman 1
1 G-SCOP_OC - Optimisation Combinatoire
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : Moemke and Svensson presented a beautiful new approach for the traveling salesman problemon a graph metric (graph-TSP), which yields a 4/3-approximation guarantee on subcubic graphsas well as a substantial improvement over the 3/2-approximation guarantee of Christofides’algorithm on general graphs. The crux of their approach is to compute an upper bound on theminimum cost of a circulation in a particular network,C(G, T), whereGis the input graphandTis a carefully chosen spanning tree. The cost of this circulation is directly related tothe number of edges in a tour output by their algorithm. Mucha subsequently improved theanalysis of the circulation cost, proving that Moemke and Svensson’s algorithm for graph-TSPhas an approximation ratio of at most 13/9 on general graphs. This analysis of the circulation is local, and vertices with degree four or five can contributethe most to its cost. Thus, hypothetically, there could exist a subquartic graph (a graph withdegree at most four at each vertex) for which Mucha’s analysis of the M ̈omke-Svensson algorithmis tight. We show that this is not the case and that M ̈omke and Svensson’s algorithm for graph-TSP has an approximation guarantee of at most 25/18 on subquartic graphs. To prove this,we present different methods to upper bound the minimum cost of a circulation on the networkC(G, T). Our approximation guarantee holds for all graphs that have an optimal solution for astandard linear programming relaxation of graph-TSP with subquartic support.
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Contributor : Alantha Newman <>
Submitted on : Thursday, January 7, 2021 - 11:43:08 AM
Last modification on : Friday, January 8, 2021 - 3:37:41 AM

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Alantha Newman. An Improved Analysis of the Mömke--Svensson Algorithm for Graph-TSP on Subquartic Graphs (Journal Version). SIAM Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2020, 34 (1), pp.865-884. ⟨10.1137/19M1259353⟩. ⟨hal-03049522⟩

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