Binary Steiner Trees: Structural Results and an Exact Solution Approach

Journal article
(Original article)


Publication Details

Author(s): Liers F, Martin A, Pape S
Journal: Discrete Optimization
Publisher: Elsevier
Publication year: 2016
Volume: 21
Pages range: 85-117
ISSN: 1572-5286
Language: English


Abstract


In this paper we study the Steiner tree problem with degree constraints. Motivated by an application in computational biology we focus on binary Steiner trees in which all node degrees are required to be at most three. It is shown that finding a binary Steiner tree is NP-complete for arbitrary graphs. We relate the problem to Steiner trees without degree constraints as well as degree-constrained spanning trees by proving approximation ratios. Further, we give integer programming formulations for this problem on undirected and directed graphs and study the associated polytopes for both cases. Some classes of facets are introduced. Based on this study a branch-&-cut approach is developed and evaluated on biological instances coming from the reconstruction of phylogenetic trees. We are able to solve nearly all instances up to 200 nodes to optimality within a limited amount of time. This shows the effectiveness of our approach.



FAU Authors / FAU Editors

Liers-Bergmann, Frauke Prof. Dr.
Professur für Angewandte Mathematik (Ganzzahlige und robuste Optimierung)
Martin, Alexander Prof. Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Pape, Susanne
Economics - Discrete Optimization - Mathematics (EDOM)


Additional Organisation
Economics - Discrete Optimization - Mathematics (EDOM)


How to cite

APA:
Liers, F., Martin, A., & Pape, S. (2016). Binary Steiner Trees: Structural Results and an Exact Solution Approach. Discrete Optimization, 21, 85-117. https://dx.doi.org/10.1016/j.disopt.2016.05.006

MLA:
Liers, Frauke, Alexander Martin, and Susanne Pape. "Binary Steiner Trees: Structural Results and an Exact Solution Approach." Discrete Optimization 21 (2016): 85-117.

BibTeX: 

Last updated on 2018-17-10 at 13:20