On the minimum diameter cost-constrained steiner tree problem

Wei Ding, Guoliang Xue

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant C 0 ≥ 0, the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by C 0. The diameter of tree refers to the maximum weight of the paths connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a (1 + ε)-approximation of the restricted version problem for any ε > 0 with specific characteristic.

Original languageEnglish (US)
Title of host publicationCombinatorial Optimization and Applications - 6th International Conference, COCOA 2012, Proceedings
Pages37-48
Number of pages12
DOIs
StatePublished - Aug 20 2012
Event6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012 - Banff, AB, Canada
Duration: Aug 5 2012Aug 9 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7402 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012
CountryCanada
CityBanff, AB
Period8/5/128/9/12

Keywords

  • Minimum diameter
  • cost-constrained Steiner tree
  • fixed topology
  • weakly fully polynomial time approximation scheme

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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