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      The network design problem with relays

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      Author(s)
      Cabral, E. A.
      Erkut, E.
      Laporte, G.
      Patterson, R. A.
      Date
      2007
      Source Title
      European Journal of Operational Research
      Print ISSN
      0377-2217
      Electronic ISSN
      1872-6860
      Publisher
      Elsevier
      Volume
      180
      Issue
      2
      Pages
      834 - 844
      Language
      English
      Type
      Article
      Item Usage Stats
      229
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      241
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      Abstract
      The network design problem with relays (NDPR) is defined on an undirected graph G = (V, E, K), where V = {1, ..., n} is a vertex set, E = {(i, j) : i, j ∈ V, i < j} is an edge set. The set K = {(o(k), d(k))} is a set of communication pairs (or commodities): o(k) ∈ V and d(k) ∈ V denote the origin and the destination of the kth commodity, respectively. With each edge (i, j) are associated a cost cij and a length dij. With vertex i is associated a fixed cost fi of locating a relay at i. The NDPR consists of selecting a subset over(E, -) of edges of E and of locating relays at a subset over(V, -) of vertices of V in such a way that: (1) the sum Q of edge costs and relay costs is minimized; (2) there exists a path linking the origin and the destination of each commodity in which the length between the origin and the first relay, the last relay and the destination, or any two consecutive relays does not exceed a preset upper bound λ. This article develops a lower bound procedure and four heuristics for the NPDR. These are compared on several randomly generated instances with |V| ≤ 1002 and |E| ≤ 1930.
      Keywords
      Column generation
      Heuristic
      Network design
      Telecommunications
      Costs
      Problem solving
      Set theory
      Telecommunication systems
      Design problems
      Graph theory
      Permalink
      http://hdl.handle.net/11693/23426
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.ejor.2006.04.030
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