An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks

Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33-approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known lower bound for this algorithm.

[1]  Reuven Bar-Yehuda,et al.  Multiple Communication in Multihop Radio Networks , 1993, SIAM J. Comput..

[2]  Andrea E.F. Clementiy,et al.  A Worst-case Analysis of an MST-based Heuristic to Construct Energy-Efficient Broadcast Trees in Wireless Networks , 2007 .

[3]  Alfredo Navarra,et al.  Tighter bounds for the minimum energy broadcasting problem , 2005, Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt'05).

[4]  Anthony Ephremides,et al.  Energy-Efficient Broadcast and Multicast Trees in Wireless Networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[5]  H. Pollak,et al.  Steiner Minimal Trees , 1968 .

[6]  Samir Khuller,et al.  Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets , 1998, FSTTCS.

[7]  Andrzej Pelc,et al.  Power consumption in packet radio networks , 2000, Theor. Comput. Sci..

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

[9]  Reuven Bar-Yehuda,et al.  On the Time-Complexity of Broadcast in Multi-hop Radio Networks: An Exponential Gap Between Determinism and Randomization , 1992, J. Comput. Syst. Sci..

[10]  J. Michael Steele.  Cost of sequential connection for points in space , 1989 .

[11]  R. Montemanni,et al.  Mathematical models and exact algorithms for the min-power symmetric connectivity problem: an overview , 2004 .

[12]  Gregory Lauer,et al.  Packet-radio routing , 1995 .

[13]  Xiang-Yang Li,et al.  Minimum-energy broadcast routing in static ad hoc wireless networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[14]  Stéphane Pérennes,et al.  Improved Approximation Results for the Minimum Energy Broadcasting Problem , 2007, Algorithmica.

[15]  Zygmunt J. Haas,et al.  On some challenges and design choices in ad-hoc communications , 1998, IEEE Military Communications Conference. Proceedings. MILCOM 98 (Cat. No.98CH36201).

[16]  Andrea E. F. Clementi,et al.  On the approximation ratio of the MST based heuristic for the energy-efficient broadcast problem in static ad-hoc radio networks , 2003, Proceedings International Parallel and Distributed Processing Symposium.

[17]  Reuven Bar-Yehuda,et al.  Multiple communication in multi-hop radio networks , 1989, PODC '89.

[18]  Kaveh Pahlavan,et al.  Wireless Information Networks , 1995 .

[19]  Andrea E. F. Clementi,et al.  Some Recent Theoretical Advances and Open Questions on Energy Consumption in Ad-Hoc Wireless Networks , 2001 .

[20]  Stéphane Pérennes,et al.  The "Real" Approximation Factor of the MST Heuristic for the Minimum Energy Broadcasting , 2005, WEA.

[21]  Andrea E. F. Clementi,et al.  On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs , 2001, STACS.

[22]  Stéphane Pérennes,et al.  Adaptive Broadcast Consumption (ABC), a New Heuristic and New Bounds for the Minimum Energy Broadcast Routing Problem , 2004, NETWORKING.