# A subexponential parameterized algorithm for Subset TSP on planar graphs

Klein, PN and Marx, Dániel
(2014)
*A subexponential parameterized algorithm for Subset TSP on planar graphs.*
In:
25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014.
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
.
Association for Computing Machinery, New York, pp. 1812-1830.
ISBN 9781611973389

Text
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## Abstract

Given a graph G and a subset S of vertices, the Subset TSP problem asks for a shortest closed walk in G visiting all vertices of S. The problem can be solved in time 2k · nO(1) using the classical dynamic programming algorithms of Bellman and of Held and Karp, where k = |S| and n = | V(G)|. Our main result is showing that the problem can be solved in time (2O(√k log k)+ W) · nO(1) if G is a planar graph with weights that are integers no greater than W. While similar speedups have been observed for various paramterized problems 011 planar graphs, our result cannot be simply obtained as a consequence of bounding the treewidth of G or invoking bidimensionality theory. Our algorithm consists of two steps: (1) find a locally optimal solution, and (2) use it to guide a dynamic program. The proof of correctness of the algorithm depends on a treewidth bound on a graph obtained by combining an optimal solution with a locally optimal solution. Copyright © 2014 by the Society for Industrial and Applied Mathematics.

Item Type: | Book Section |
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Uncontrolled Keywords: | Graph theory; TSP problems; Proof of correctness; planar graph; Parameterized algorithm; Optimal solutions; Dynamic programs; Classical dynamics; Bidimensionality theory; Optimal systems; Graphic methods; dynamic programming; Algorithms |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 26 Sep 2014 19:17 |

Last Modified: | 26 Sep 2014 19:17 |

URI: | https://eprints.sztaki.hu/id/eprint/8002 |

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