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

Authors:
Valeria Leggieri;Mohamed Haouari;Chefi Triki
Affiliations:
Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bolzano, Italy and Dipartimento di Matematica, Universití del Salento, 73100 Lecce, Italy;Combinatorial Optimization Research Group, ROI, Ecole Polytechnique de Tunisie, BP 743, 2078 La Marsa, Tunisia and Department of Industrial Engineering, Faculty of Engineering, Ozyegin University, ...;Dipartimento di Matematica, Universití del Salento, 73100 Lecce, Italy
Venue:
Discrete Applied Mathematics
Year:
2014

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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.