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Minimum power multicasting problem in wireless networks

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Abstract

In this paper we deal with the minimum power multicasting (MPM) problem in wireless ad-hoc networks. By using an appropriate choice of the decision variables and by exploiting the topological properties of the problem, we are able to define an original formulation based on a Set Covering model. Moreover, we propose for its solution two exact procedures that include a preprocessing technique that reduces the huge number of the model’s constraints. We also report some experimental results carried out on a set of randomly generated test problems.

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References

  • Althaus E, Călinescu G, Măndoiu II, Prasad S, Tchervenski N, Zelikovsky A (2003) Power efficient range assignment in ad-hoc wireless networks. Proc IEEE WCNC’03:1889–1894

    Google Scholar 

  • Altinkemer K, Salman FS, Bellur P (2005) Solving the minimum energy broadcasting problem in ad hoc wireless networks by integer programming. Proc INOC 2005(B2): 635–642

    Google Scholar 

  • Cagalj M, Hubaux JP, Enz C (2002) Minimum-energy broadcast in all-wireless networks: NP-completeness and distribution issues. In: Proceedings of the MOBICOM

  • Clementi A, Penna P, Silvestri R (1999) Hardness results for the power range assignment problem in packet radio networks. Lect Notes Comput Sci 1671: 195–208

    Google Scholar 

  • Clementi A, Crescenzi P, Penna P, Rossi G, Vocca P (2001) On the complexity of computing minimum energy consumption broadcast subgraphs. In: Symposium on theoretical aspects of computer science, pp 121–131

  • Das AK, Marks RJ, El-Sharkawi M, Arabshani P, Gray A (2003) Minimum power broadcast trees for wireless networks: integer programming formulations. In: Proceedings of the IEEE INFOCOM conference

  • Dongarra JJ (2004) Performance of various computers using standard linear equations software. Technical report CS-89-85

  • Guo S, Yang O (2004) Optimal tree construction for minimum-energy multicast in wireless ad hoc networks. In: Proceedings of the ICNP conference

  • Leino J (2002) Optimal multicast routing in ad hoc networks. Technical report

  • Liang W (2002) Constructing minimum-energy broadcast trees in wireless ad hoc networks. In: Proceedings of the MOBIHOC’02, pp 112–122

  • Magnanti TL, Wolsey L (1995) Optimal trees. In: Ball MO et al (eds) Network models. North Holland, Amsterdam, pp 503–615

  • Montemanni R, Gambardella LM (2004) Exact algorithms for the minimum power symmetric connectivity problem in wireless networks. Comput Oper Res 31: 1667–1680

    Article  MATH  MathSciNet  Google Scholar 

  • Montemanni R, Leggieri V, Triki C (2008) Mixed integer formulations for the probabilistic minimum energy broadcast problem in wireless networks. Eur J Oper Res (in press). doi:10.1016/j.ejor.2007.06.031

  • Oliveira CAS, Pardalos PM (2005) A survey of combinatorial optimization problems in multicast routing. Comput Oper Res 32:1953–1981

    Article  MATH  Google Scholar 

  • Padberg M, Wolsey L (1983) Trees and cuts. Ann Discr Math 17: 511–517

    MATH  MathSciNet  Google Scholar 

  • Rappaport T (1996) Wireless communications: principles and practices. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Wan PJ, Călinescu G, Li XY, Frieder O (2001) Minimum energy broadcast routing in static ad hoc wireless networks. In: Proceedings of the IEEE infocom, pp 1162–1171

  • Wieselthier JE, Nguyen G, Ephremides A (2001) Algorithms for energy-efficient multicasting in static ad hoc networks. Mobile Netw Appl 6: 251–263

    Article  MATH  Google Scholar 

  • Wieselthier JE, Nguyen G, Ephremides A (2000) On the construction of energy-efficient broadcast and multicast trees in wireless networks. In: Proceedings of the IEEE INFOCOM 2000 conference

  • Yuan D (2005) An integer programming approach for the minimum-energy broadcast problem in wireless networks. Proc INOC B2: 643–650

    Google Scholar 

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Correspondence to Valeria Leggieri.

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Leggieri, V., Nobili, P. & Triki, C. Minimum power multicasting problem in wireless networks. Math Meth Oper Res 68, 295–311 (2008). https://doi.org/10.1007/s00186-008-0222-0

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