The parameterized complexity of local search for TSP, more refined

Authors:
Jiong Guo;Sepp Hartung;Rolf Niedermeier;Ondřej Suchý
Affiliations:
Universität des Saarlandes, Saarbrücken, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Universität des Saarlandes, Saarbrücken, Germany
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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Abstract

We extend previous work on the parameterized complexity of local search for the Travelling Salesperson Problem (TSP). So far, its parameterized complexity has been investigated with respect to the distance measures (which define the local search area) "Edge Exchange" and "Max-Shift". We perform studies with respect to the distance measures "Swap" and "m-Swap", "Reversal" and "m-Reversal", and "Edit", achieving both fixed-parameter tractability and W[1]-hardness results. 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.