Elsevier

Journal of Algorithms

Volume 38, Issue 2, February 2001, Pages 411-437
Journal of Algorithms

Regular Article
On Minimum Edge Ranking Spanning Trees

https://doi.org/10.1006/jagm.2000.1143Get rights and content

Abstract

In this paper, we introduce the problem of computing a minimum edge ranking spanning tree (MERST); i.e., find a spanning tree of a given graph G whose edge ranking is minimum. Although the minimum edge ranking of a given tree can be computed in polynomial time, we show that problem MERST is NP-hard. Furthermore, we present an approximation algorithm for MERST, which realizes its worst case performance ratiominΔ*1logn/Δ*,Δ*1logΔ*+11where n is the number of vertices in G and Δ* is the maximum degree of a spanning tree whose maximum degree is minimum. Although the approximation algorithm is a combination of two existing algorithms for the restricted spanning tree problem and for the minimum edge ranking problem of trees, the analysis is based on novel properties of the edge ranking of trees.

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This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan under Grant 11750353.

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