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The Covering Canadian Traveller Problem Revisited

Authors Niklas Hahn , Michalis Xefteris

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Online Algorithm
  • Canadian Traveller Problem
  • Travelling Salesperson Problem
  • Graph Exploration

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Abstract

In this paper, we consider the k-Covering Canadian Traveller Problem (k-CCTP), which can be seen as a variant of the Travelling Salesperson Problem. The goal of k-CCTP is finding the shortest tour for a traveller to visit a set of locations in a given graph and return to the origin. Crucially, unknown to the traveller, up to k edges of the graph are blocked and the traveller only discovers blocked edges online at one of their respective endpoints. The currently best known upper bound for k-CCTP is O(√k) which was shown in [Huang and Liao, ISAAC '12]. We improve this polynomial bound to a logarithmic one by presenting a deterministic O(log k)-competitive algorithm that runs in polynomial time. Further, we demonstrate the tightness of our analysis by giving a lower bound instance for our algorithm.

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Niklas Hahn and Michalis Xefteris. The Covering Canadian Traveller Problem Revisited. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 53:1-53:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.53

Author Details

Niklas Hahn
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Michalis Xefteris
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

Funding

This work was partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).

Acknowledgements

We would like to thank Evripidis Bampis and Bruno Escoffier for providing useful comments on the manuscript.

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