DROPS

Document

DOI: 10.4230/LIPIcs.SWAT.2026.18

On Fréchet Traveling Salesmen Problems

Authors: Omrit Filtser, Tzalik Maimon, and Michal Moiseev

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

The Fréchet distance is a well-studied distance measure between two curves. In this work, we demonstrate that the merit of Fréchet distance extends beyond evaluating similarity, and introduce a new setting in which it proves useful. Consider a situation where two agents are required to visit a given set of sites, while staying close to each other throughout their traversal. In this paper, we study problems where the goal is to construct two curves whose vertices are from a given set of points, under the constraint that the Fréchet distance between the curves is kept as small as possible. This problem can be viewed as a variant of the Traveling Salesman Problem (TSP), and thus may be of interest in routing, network planning and more. We present a near-linear algorithm for this problem under the discrete Fréchet distance, and explore several variants of the problem, including minimizing the lengths of the curves and balancing the number of sites assigned to each agent. Lastly, we prove that the problem is NP-hard under the continuous Fréchet Distance.

Cite as

Omrit Filtser, Tzalik Maimon, and Michal Moiseev. On Fréchet Traveling Salesmen Problems. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{filtser_et_al:LIPIcs.SWAT.2026.18,
  author =	{Filtser, Omrit and Maimon, Tzalik and Moiseev, Michal},
  title =	{{On Fr\'{e}chet Traveling Salesmen Problems}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.18},
  URN =		{urn:nbn:de:0030-drops-260545},
  doi =		{10.4230/LIPIcs.SWAT.2026.18},
  annote =	{Keywords: Fr\'{e}chet distance, traveling salesman problem}
}

Search Results

Documents authored by Moiseev, Michal

On Fréchet Traveling Salesmen Problems

Abstract

Cite as

Thanks for your feedback!

Could not send message