An efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection

Refael Hassin*, Asaf Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Given an undirected graph G = (V, E) with |V| = n and |E| = m, nonnegative integers ce and de for each edge e ∈ E, and a bound D, the constrained minimum spanning tree problem (CST) is to find a spanning tree T = (V, ET) such that Σe ∈ E T d e ≤ D and Σe∈E T ce is minimized. We present an efficient polynomial time approximation scheme (EPTAS) for this problem. Specifically, for every ε > 0 we present a (1 + ε)-approximation algorithm with time complexity O((1/ε) O(1/ε) n4). Our method is based on Lagrangian relaxation and matroid intersection.

Original languageEnglish
Pages (from-to)261-268
Number of pages8
JournalSIAM Journal on Computing
Volume33
Issue number2
DOIs
StatePublished - Jan 2004

Keywords

  • Approximation algorithm
  • Bicriteria optimization
  • Matroid intersection
  • Spanning tree

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