The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

Valeria Leggieri*, Mohamed Haouari, Chefi Triki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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
Issue numberPART 1
Publication statusPublished - 2014


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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