Minimum diameter cost-constrained Steiner trees

Wei Ding, Guoliang Xue

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Given an edge-weighted undirected graph G=(V,E,c,w) where each edge eεE has a cost c(e)≥0 and another weight w(e)≥0, a set S⊂ V of terminals and a given constant \mathrm{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 \mathrm{C}-0. The diameter of a tree refers to the maximum weight of the path 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 a specific characteristic.

Original languageEnglish (US)
Pages (from-to)32-48
Number of pages17
JournalJournal of Combinatorial Optimization
Volume27
Issue number1
DOIs
StatePublished - Jan 1 2014

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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