2026-07-25T14:45:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:21162 2024-09-23T09:13:18Z ddc:004 open_access

Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm Nie, Zipei Zhou, Hang capacitated vehicle routing approximation algorithm combinatorial optimization We study the unit-demand capacitated vehicle routing problem in the random setting of the Euclidean plane. The objective is to visit n random terminals in a square using a set of tours of minimum total length, such that each tour visits the depot and at most k terminals. We design an algorithm combining the classical sweep heuristic and the framework for the Euclidean traveling salesman problem due to Arora [J. ACM 1998] and Mitchell [SICOMP 1999]. We show that our algorithm is a polynomial-time approximation of ratio at most 1.55 asymptotically almost surely. This improves on the prior ratio of 1.915 due to Mathieu and Zhou [RSA 2022]. In addition, we conjecture that, for any ε > 0, our algorithm is a (1+ε)-approximation asymptotically almost surely. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Zipei Nie and Hang Zhou 2024 Is Part Of LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2024.91 urn:nbn:de:0030-drops-211627 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.91 eng https://creativecommons.org/licenses/by/4.0/legalcode