TSP in a Simple Polygon.

Henk Alkema; Mark de Berg; Morteza Monemizadeh; Leonidas Theocharous

doi:10.4230/LIPIcs.ESA.2022.5

TSP in a Simple Polygon.

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

Abstract

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) + 2O(√ n log 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.

Original language	English
Title of host publication	30th Annual European Symposium on Algorithms, ESA 2022
Editors	Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Herman
Pages	5:1-5:14
Number of pages	14
ISBN (Electronic)	9783959772471
DOIs	https://doi.org/10.4230/LIPIcs.ESA.2022.5
Publication status	Published - 1 Sept 2022

Bibliographical note

DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

Keywords

Subexponential algorithms
TSP with obstacles
Traveling Salesman Problem

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10.4230/LIPIcs.ESA.2022.5

Cite this

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title = "TSP in a Simple Polygon.",

abstract = "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) + 2O(√ n log 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.",

keywords = "Subexponential algorithms, TSP with obstacles, Traveling Salesman Problem",

author = "Henk Alkema and Berg, {Mark de} and Morteza Monemizadeh and Leonidas Theocharous",

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AU - Berg, Mark de

AU - Monemizadeh, Morteza

AU - Theocharous, Leonidas

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PY - 2022/9/1

Y1 - 2022/9/1

N2 - 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) + 2O(√ n log 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.

AB - 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) + 2O(√ n log 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.

KW - Subexponential algorithms

KW - TSP with obstacles

KW - Traveling Salesman Problem

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U2 - 10.4230/LIPIcs.ESA.2022.5

DO - 10.4230/LIPIcs.ESA.2022.5

M3 - Conference contribution

SP - 5:1-5:14

BT - 30th Annual European Symposium on Algorithms, ESA 2022

A2 - Chechik, Shiri

A2 - Navarro, Gonzalo

A2 - Rotenberg, Eva

A2 - Herman, Grzegorz

ER -

TSP in a Simple Polygon.

Abstract

Bibliographical note

Keywords

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