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  • 1.
    Bauer, J.
    et al.
    Department of Informatics, University of Bergen, N-5020 Bergen, Norway.
    Haugland, D.
    Department of Informatics, University of Bergen, N-5020 Bergen, Norway.
    Yuan, D.
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Communications and Transport Systems.
    Analysis and computational study of several integer programming formulations for minimum-energy multicasting in wireless ad hoc networks2008In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 52, no 2, p. 57-68Article in journal (Refereed)
    Abstract [en]

    A multicast session in a wireless ad hoc network concerns routing messages from a source to a set of destination devices. Transmitting messages consumes energy at the source and intermediate devices of the session. Since a battery is the only energy source in many applications of wireless ad hoc networks, energy efficiency is an important performance measure of multicasting. In this paper, we present and analyze integer programming models for the problem of minimizing the total energy required by multicasting. We start from a straightforward multicommodity flow model, which is strengthened by a more efficient representation of transmission power. Further strengthening is accomplished by lifting the capacity constraints of the model. We then present cut-based models for the problem, and prove, from a bounding standpoint, the equivalence in strength between these models and their flow-based counterparts. By expanding the underlying graph, we show that the problem can be transformed into finding a minimum Steiner arborescence. The expanded graph arises also in the separation procedure for solving one of the cut-based models. In addition to a theoretical analysis of the relation between various models, we perform extensive computational experiments to study the numerical strengths of these models and their efficiency in solving the problem. © 2008 Wiley Periodicals, Inc.

  • 2.
    Broström, Peter
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Valid Cycles: A Source of Infeasibility in Open Shortest Path First Routing2008In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 52, no 4, p. 206-215Article in journal (Refereed)
    Abstract [en]

    Many telecommunication networks use the open shortest path first (OSPF) protocol for the routing of traffic. In such networks, each router sends the traffic on the shortest paths to the destination, with respect to the link weights assigned. An interesting question is whether or not a set of desired routing patterns can be obtained in an OSPF network by assigning appropriate weights. If not, we wish to find the source of the infeasibility. We study these issues by formulating a mathematical model and investigating its feasibility. A certain structure, called valid cycle, is found to be present in most infeasible instances. This yields new necessary conditions, stronger than those previously known, for the existence of weights yielding a set of given desired shortest path graphs. A valid cycle indicates which parts of the routing patterns are in conflict and can be used for changing the routing patterns to make the problem feasible. A polynomial algorithm for finding valid cycles is presented, the method is illustrated by a numerical example, and computational tests are reported.

  • 3. Engevall, Stefan
    et al.
    Göthe-Lundgren, Maud
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Värbrand, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    A strong lower bound for the node weighted Steiner tree problem1998In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 31, p. 11-17Article in journal (Refereed)
  • 4.
    Holmberg, Kaj
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Yuan, Di
    Linköping University, Department of Science and Technology.
    Optimization of Internet Protocol Network Design and Routing2004In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 43, no 1, p. 39-53Article in journal (Refereed)
    Abstract [en]

    We consider network design and routing for Internet Protocol (IP) traffic. The design problem concerns capacity dimensioning of communication links, where the design cost consists of fixed charges and linear capacity expansion costs. The optimization problem also concerns determining the amount of traffic demand to be carried by the network and the metric used by a shortest path routing protocol. We present a novel linear mixed-integer mathematical formulation and two heuristic solution procedures. The first heuristic uses mixed-integer programming to generate a sequence of routing solutions. The second solution approach is a simulated annealing meta heuristic. Computational experiments for synthesized and real-life networks show that high-quality solutions can be obtained by both approaches.

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