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1991•SIAM Journal on ComputingRequires access

Minimum Diameter Spanning Trees and Related Problems

Jan-Ming Ho, D. T. Lee, Chia-Hsiang Chang, C. K. Wong

Open publisher page 86 citations

Abstract

The problem of finding a minimum diameter spanning tree (MDST) of a set of n points in the Euclidean space is considered. The diameter of a spanning tree is the maximum distance between any two points in the tree. A characterization of an MDST is given and a $\theta (n^3)$-time algorithm for solving the problem is presented. The authors also show that for a weighted undirected graph, the problem of determining if a spanning tree with total weight and diameter upper bounded, respectively, by two given parameters C and D exists is NP-complete. The geometric Steiner minimum diameter spanning tree problem, in which new points are allowed to be part of the spanning tree, is shown to be solvable in $O(n)$ time.

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What this paper is about

The problem of finding a minimum diameter spanning tree (MDST) of a set of n points in the Euclidean space is considered. The diameter of a spanning tree is the maximum distance between any two points in the tree. A characterization of an MDST is given and a $\theta (n^3)$-time algorithm for solving the problem is presented. The authors also show that for a weighted undirected graph, the problem of determining if a spanning tree with total weight and diameter upper bounded, respectively, by two given parameters C and D exists is NP-complete. The geometric Steiner minimum diameter spanning tree problem, in which new points are allowed to be part of the spanning tree, is shown to be solvable in $O(n)$ time.

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OpenAlex reports 86 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The problem of finding a minimum diameter spanning tree (MDST) of a set of n points in the Euclidean space is considered. The diameter of a spanning tree is the maximum distance between any two points in the tree. A characterization of an MDST is given and a $\theta (n^3)$-time algorithm for solving the problem is presented. The authors also show that for a weighted undirected graph, the problem of determining if a spanning tree with total weight and diameter upper bounded, respectively, by two given parameters C and D exists is NP-complete. The geometric Steiner minimum diameter spanning tree problem, in which new points are allowed to be part of the spanning tree, is shown to be solvable in $O(n)$ time.

Key concepts: Spanning tree, Euclidean minimum spanning tree, Minimum spanning tree, k-minimum spanning tree, Combinatorics, Shortest-path tree, Connected dominating set, Minimum degree spanning tree

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