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The Parameterized Complexity of Local Search for TSP, More Refined

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Abstract

We extend previous work on the parameterized complexity of local search for the Traveling Salesperson Problem (TSP). So far, its parameterized complexity has been investigated with respect to the distance measures (defining the local search area) “Edge Exchange” and “Max-Shift”. We perform studies with respect to the distance measures “Swap” and “r-Swap”, “Reversal” and “r-Reversal”, and “Edit”, achieving both fixed-parameter tractability and W[1]-hardness results. In particular, from the parameterized reduction showing W[1]-hardness we infer running time lower bounds (based on the exponential time hypothesis) for all corresponding distance measures. Moreover, we provide non-existence results for polynomial-size problem kernels and we show that some in general W[1]-hard problems turn fixed-parameter tractable when restricted to planar graphs.

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Notes

  1. The reversal distance is also widely studied in bioinformatics in the context of genome rearrangements [6, 15].

  2. Roughly speaking, the ETH states that 3-Sat cannot be solved in subexponential time.

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Authors and Affiliations

  1. Cluster of Excellence, Multimodal Computing and Interaction, Universität des Saarlandes, Saarbrücken, Germany

    Jiong Guo

  2. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    Sepp Hartung, Rolf Niedermeier & Ondřej Suchý

Authors
  1. Jiong Guo
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  2. Sepp Hartung
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  3. Rolf Niedermeier
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  4. Ondřej Suchý
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Corresponding author

Correspondence to Sepp Hartung.

Additional information

The first and the fourth author were supported by the DFG Cluster of Excellence on Multimodal Computing and Interaction (MMCI) and the DFG project DARE (GU 1023/1-2). Most of the work of Ondřej Suchý was done while he was with MMCI Saarbrücken.

An extended abstract of this paper appeared in Proceedings of the 22nd International Symposium on Algorithms and Computation (ISAAC’11), Yokohama, Japan, Dec. 2011, volume 7074 of LNCS, pages 614–623, Springer, 2011. An important difference compared to the conference version is that we significantly improved the running time lower bounds.

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Guo, J., Hartung, S., Niedermeier, R. et al. The Parameterized Complexity of Local Search for TSP, More Refined. Algorithmica 67, 89–110 (2013). https://doi.org/10.1007/s00453-012-9685-8

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