eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-09-01
5:1
5:14
10.4230/LIPIcs.ESA.2022.5
article
TSP in a Simple Polygon
Alkema, Henk
1
de Berg, Mark
1
https://orcid.org/0000-0001-5770-3784
Monemizadeh, Morteza
1
Theocharous, Leonidas
1
Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol244-esa2022/LIPIcs.ESA.2022.5/LIPIcs.ESA.2022.5.pdf
Traveling Salesman Problem
Subexponential algorithms
TSP with obstacles