Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem

Authors:
Keizo Miyata;Shigeru Masuyama;Shin-ichi Nakayama;Liang Zhao
Affiliations:
Knowledge-Based Information Engineering, Toyohashi University of Technology, Toyohashi, Japan;Knowledge-Based Information Engineering, Toyohashi University of Technology, Toyohashi, Japan;Mathematical Sciences, Faculty Integrated Arts and Sciences, The University of Tokushima, Tokushima, Japan;Department of Information Science, Faculty of Engineering, Utsunomiya University, Utsunomiya, Japan
Venue:
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Year:
2006

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Abstract

The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a (⌈Ds/2⌉ + 1)/(⌊log2(Ds + 1)⌋ + 1)-approximation algorithm for MVRST where Ds is the minimum diameter of spanning trees of G.