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

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      Author
      Akgün, I.
      Tansel, B. Ç.
      Date
      2011
      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
      Item Usage Stats
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      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).
      Keywords
      Graph theory
      Integer programming
      Spanning trees
      Hop constraints
      Miller–Tucker–Zemlin constraints
      Permalink
      http://hdl.handle.net/11693/21856
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.ejor.2011.01.051
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      • Department of Industrial Engineering 677
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