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<p>Given a set <i>P</i> of <i>n</i> 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(n^2)\)</EquationSource> </InlineEquation> time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(O(n^{4/3} \log ^3 n)\)</EquationSource> </InlineEquation> time.</p>

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Computing the Minimum Bottleneck Moving Spanning Tree

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • Haitao Wang,
  • Yiming Zhao

摘要

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 \(O(n^2)\) time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of \(O(n^{4/3} \log ^3 n)\) time.