The Steiner Tree Problem with Delays

A compact formulation and reduction procedures

Valeria Leggieri, Mohamed Haouari, Chefi Triki

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper investigates the Steiner Tree Problem with Delays (STPD), a variation of the classical Steiner Tree problem that arises in multicast routing. We propose an exact solution approach that is based on a polynomial-size formulation for this challenging NP-hard problem. The LP relaxation of this formulation is enhanced through the derivation of new lifted Miller-Tucker-Zemlin subtour elimination constraints. Furthermore, we present several preprocessing techniques for both reducing the problem size and tightening the LP relaxation. Finally, we report the results of extensive computational experiments on instances with up to 1000 nodes. These results attest to the efficacy of the combination of the enhanced formulation and reduction techniques.

Original languageEnglish
Pages (from-to)178-190
Number of pages13
JournalDiscrete Applied Mathematics
Volume164
Issue numberPART 1
DOIs
Publication statusPublished - 2014

Fingerprint

Steiner Tree Problem
LP Relaxation
Computational complexity
Polynomials
Formulation
Multicast Routing
Experiments
NP-hard Problems
Computational Experiments
Preprocessing
Elimination
Efficacy
Exact Solution
Polynomial
Vertex of a graph

Keywords

  • MTZ subtour elimination constraints
  • Reduction techniques
  • Steiner tree problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

The Steiner Tree Problem with Delays : A compact formulation and reduction procedures. / Leggieri, Valeria; Haouari, Mohamed; Triki, Chefi.

In: Discrete Applied Mathematics, Vol. 164, No. PART 1, 2014, p. 178-190.

Research output: Contribution to journalArticle

Leggieri, Valeria ; Haouari, Mohamed ; Triki, Chefi. / The Steiner Tree Problem with Delays : A compact formulation and reduction procedures. In: Discrete Applied Mathematics. 2014 ; Vol. 164, No. PART 1. pp. 178-190.
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