Computing the Minimum Bottleneck Moving Spanning Tree

Haitao Wang

doi:10.1007/s00453-025-01358-0

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Computing the Minimum Bottleneck Moving Spanning Tree

2025-11-14

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Haitao Wang

Yiming Zhao *

DOI：10.1007/s00453-025-01358-0

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Abstract

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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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n<^>2)$$\end{document} time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n<^>{4/3} \log <^>3 n)$$\end{document} time.

Keywords:

Minimum spanning tree

Moving points

Unit-disk range emptiness query

Dynamic data structure