TSP in a Simple Polygon

Authors Henk Alkema, Mark de Berg , Morteza Monemizadeh, Leonidas Theocharous

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Author Details

Henk Alkema
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Mark de Berg
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Morteza Monemizadeh
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Leonidas Theocharous
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands

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Henk Alkema, Mark de Berg, Morteza Monemizadeh, and Leonidas Theocharous. TSP in a Simple Polygon. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We study the Traveling Salesman Problem inside a simple polygon. In this problem, which we call tsp in a simple polygon, we wish to compute a shortest tour that visits a given set S of n sites inside a simple polygon P with m edges while staying inside the polygon. This natural problem has, to the best of our knowledge, not been studied so far from a theoretical perspective. It can be solved exactly in poly(n,m) + 2^O(√nlog n) time, using an algorithm by Marx, Pilipczuk, and Pilipczuk (FOCS 2018) for subset tsp as a subroutine. We present a much simpler algorithm that solves tsp in a simple polygon directly and that has the same running time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Traveling Salesman Problem
  • Subexponential algorithms
  • TSP with obstacles


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