New formulations of the hop-constrained minimum spanning tree problem via Miller-Tucker-Zemlin constraints

Date
2011
Authors
Akgün, I.
Tansel, B. Ç.
Advisor
Instructor
Source Title
European Journal of Operational Research
Print ISSN
0377-2217
Electronic ISSN
1872-6860
Publisher
Elsevier
Volume
212
Issue
2
Pages
263 - 276
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

Given an undirected network with positive edge costs and a natural number p, the Hop-Constrained Minimum Spanning Tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, we develop new formulations for HMST. The formulations are based on Miller-Tucker-Zemlin (MTZ) subtour elimination constraints, MTZ-based liftings in the literature offered for HMST, and a new set of topology-enforcing constraints. We also compare the proposed models with the MTZ-based models in the literature with respect to linear programming relaxation bounds and solution times. The results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to MTZ constraints, some of which are based on well-known, strong liftings of Desrochers and Laporte (1991).

Course
Other identifiers
Book Title
Keywords
Graph theory, Integer programming, Spanning trees, Hop constraints, Miller–Tucker–Zemlin constraints
Citation
Published Version (Please cite this version)