Shorter tours by nicer ears: 7/5-Approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs

Abstract

We prove new results for approximating the graph-TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees.

For the graph-TSP itself, we improve the approximation ratio to 7=5. For a generalization, the minimum T-tour problem, we obtain the first nontrivial approximation algorithm, with ratio 3=2. This contains the s-t-path graph-TSP as a special case. Our approximation guarantee for finding a smallest 2-edge-connected spanning subgraph is 4=3.

The key new ingredient of all our algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs. The same methods also provide the lower bounds (arising from LP relaxations) that we use to deduce the approximation ratios.

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Correspondence to András Sebő.

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Supported by LabEx PERSYVAL-Lab (ANR-11-LABX-0025), and TEOMATRO (ANR-10-BLAN 0207).

This work was done while visiting Grenoble, Laboratoire G-SCOP. Support of Université Joseph Fourier is gratefully acknowledged.

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Sebő, A., Vygen, J. Shorter tours by nicer ears: 7/5-Approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs. Combinatorica 34, 597–629 (2014). https://doi.org/10.1007/s00493-014-2960-3

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Mathematics Subject Classification (2000)

  • 90C27
  • 05C85
  • 68R10