Mixed integer formulations for the probabilistic minimum energy broadcast problem in wireless networks

In this paper we study a new variant of the minimum energy broadcast (MEB) problem, namely the probabilistic MEB (PMEB). The objective of the classic MEB problem is to assign transmission powers to the nodes of a wireless network is such a way that the total energy dissipated on the network is minimized, while a connected broadcasting structure is guaranteed by the assigned transmission powers. In the new variant of the problem treated in this paper, node failure is taken into account, aiming at providing solutions with a chosen reliability level for the broadcasting structure. Three mixed integer linear programming formulations for the new problem are presented, together with efficient formulation-dependent methods for their solution. Computational results are proposed and discussed. One method emerges as the most promising one under realistic settings. It is able to handle problems with up to fifty nodes.

[1]  Shie Mannor,et al.  Probabilistic Optimization for Energy-Efficient Broadcast in All-Wireless Networks , 2005 .

[2]  Andrea E. F. Clementi,et al.  On the Power Assignment Problem in Radio Networks , 2004, Mob. Networks Appl..

[3]  Ernst Althaus,et al.  Power efficient range assignment in ad-hoc wireless networks , 2003, 2003 IEEE Wireless Communications and Networking, 2003. WCNC 2003..

[4]  Chefi Triki,et al.  Minimum power multicasting problem in wireless networks , 2008, Math. Methods Oper. Res..

[5]  Roberto Montemanni,et al.  Exact algorithms for the minimum power symmetric connectivity problem in wireless networks , 2005, Comput. Oper. Res..

[6]  Arindam Kumar Das,et al.  Minimum power broadcast trees for wireless networks: integer programming formulations , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[7]  Robert J. Marks,et al.  Minimum power broadcast trees for wireless networks: optimizing using the viability lemma , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[8]  Roberto Montemanni,et al.  An exact algorithm for the robust shortest path problem with interval data , 2004, Comput. Oper. Res..

[9]  Peter Eades,et al.  On Optimal Trees , 1981, J. Algorithms.

[10]  M. El-Sharkawi,et al.  THE MINIMUM POWER BROADCAST PROBLEM IN WIRELESS NETWORKS : AN ANT COLONY SYSTEM APPROACH , 2002 .

[11]  Roberto Montemanni,et al.  The minimum power broadcast problem in wireless networks: a simulated annealing approach , 2005, IEEE Wireless Communications and Networking Conference, 2005.

[12]  Di Yuan.  An integer programming approach for the minimum-energy broadcast problem in wireless networks , 2005 .