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On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations

Authors Václav Blažej , Pratibha Choudhary , Dušan Knop , Šimon Schierreich , Ondřej Suchý , Tomáš Valla



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Václav Blažej
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Pratibha Choudhary
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Dušan Knop
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Šimon Schierreich
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Ondřej Suchý
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Tomáš Valla
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic

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Václav Blažej, Pratibha Choudhary, Dušan Knop, Šimon Schierreich, Ondřej Suchý, and Tomáš Valla. On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 22:1-22:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ESA.2022.22

Abstract

For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today’s computation, we employ one of the most successful models of such precomputation - the kernelization. Within this framework, we focus on Traveling Salesperson Problem (TSP) and some of its generalizations. We provide a kernel for TSP with size polynomial in either the feedback edge set number or the size of a modulator to constant-sized components. For its generalizations, we also consider other structural parameters such as the vertex cover number and the size of a modulator to constant-sized paths. We complement our results from the negative side by showing that the existence of a polynomial-sized kernel with respect to the fractioning number, the combined parameter maximum degree and treewidth, and, in the case of {Subset TSP}, modulator to disjoint cycles (i.e., the treewidth two graphs) is unlikely.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Fixed parameter tractability
Keywords
  • Traveling Salesperson
  • Subset TSP
  • Waypoint Routing
  • Kernelization

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