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Improved Guarantees for the a Priori TSP

Authors Jannis Blauth , Meike Neuwohner , Luise Puhlmann , Jens Vygen

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Jannis Blauth
  • Research Inst. for Discrete Mathematics, Hausdorff Center for Math., University of Bonn, Germany
Meike Neuwohner
  • Research Inst. for Discrete Mathematics, Hausdorff Center for Math., University of Bonn, Germany
Luise Puhlmann
  • Research Inst. for Discrete Mathematics, Hausdorff Center for Math., University of Bonn, Germany
Jens Vygen
  • Research Inst. for Discrete Mathematics, Hausdorff Center for Math., University of Bonn, Germany

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Jannis Blauth, Meike Neuwohner, Luise Puhlmann, and Jens Vygen. Improved Guarantees for the a Priori TSP. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.14

Abstract

We revisit the a priori TSP (with independent activation) and prove stronger approximation guarantees than were previously known. In the a priori TSP, we are given a metric space (V,c) and an activation probability p(v) for each customer v ∈ V. We ask for a TSP tour T for V that minimizes the expected length after cutting T short by skipping the inactive customers. All known approximation algorithms select a nonempty subset S of the customers and construct a master route solution, consisting of a TSP tour for S and two edges connecting every customer v ∈ V⧵S to a nearest customer in S. We address the following questions. If we randomly sample the subset S, what should be the sampling probabilities? How much worse than the optimum can the best master route solution be? The answers to these questions (we provide almost matching lower and upper bounds) lead to improved approximation guarantees: less than 3.1 with randomized sampling, and less than 5.9 with a deterministic polynomial-time algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • A priori TSP
  • random sampling
  • stochastic combinatorial optimization

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