2026-07-23T21:52:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16880 2024-03-06T10:58:34Z ddc:004 open_access

Computing the Minimum Bottleneck Moving Spanning Tree Wang, Haitao Zhao, Yiming minimum spanning tree moving points unit-disk range emptiness query dynamic data structure Given a set P of n points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to minimize the bottleneck weight of the spanning tree (i.e., the largest Euclidean length of all edges) during the whole movement. The problem was solved in O(n²) time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of O(n^{4/3} log³ n) time. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Haitao Wang and Yiming Zhao 2022 Is Part Of LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2022.82 urn:nbn:de:0030-drops-168801 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.82 eng https://creativecommons.org/licenses/by/4.0/legalcode