Low-Energy Fault-Tolerant Bounded-Hop Broadcast in Wireless Networks

This paper studies asymmetric power assignments in wireless ad hoc networks. The temporary, unfixed physical topology of wireless ad hoc networks is determined by the distribution of the wireless nodes as well as the transmission power (range) assignment of each node. We consider the problem of <i>bounded-hop</i> <i>broadcast</i> under <i>k-fault</i> <i>resilience</i> criterion for linear and planar layout of nodes. The topology that results from our power assignment allows a broadcast operation from a wireless node <i>r</i> to any other node in at most <i>h</i> hops and is <i>k</i> -fault resistant. We develop simple approximation algorithms for the two cases and obtain the following approximation ratios: linear case-<i>O</i>(<i>k</i>); planar case-we first prove a factor of <i>O</i>(<i>k</i> <sup>3</sup>) , which is later decreased to <i>O</i>(<i>k</i> <sup>2</sup>) by a finer analysis. Finally, we show a trivial power assignment with a cost <i>O</i>(<i>h</i>) times the optimum. To the best of our knowledge, these are the first nontrivial results for this problem.

[1]  Madhav V. Marathe,et al.  Topology Control Problems under Symmetric and Asymmetric Power Thresholds , 2003, ADHOC-NOW.

[2]  A. Ephremides,et al.  Algorithms for energy-efficient multicasting in ad hoc wireless networks , 1999, MILCOM 1999. IEEE Military Communications. Conference Proceedings (Cat. No.99CH36341).

[3]  Xiaohua Jia,et al.  Power Assignment for k-Connectivity in Wireless Ad Hoc Networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[4]  Andrea E. F. Clementi,et al.  The range assignment problem in non-homogeneous static ad-hoc networks , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[5]  Archan Misra,et al.  Energy-efficient broadcast and multicast trees for reliable wireless communication , 2003, 2003 IEEE Wireless Communications and Networking, 2003. WCNC 2003..

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

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

[8]  Sy-Yen Kuo,et al.  Reliable Multicast based on k-Connected Graph , 2002, IMSA.

[9]  Anthony Ephremides,et al.  Algorithms for Energy-Efficient Multicasting in Static Ad Hoc Wireless Networks , 2001, Mob. Networks Appl..

[10]  Tamer A. ElBatt,et al.  Joint scheduling and power control for wireless ad hoc networks , 2002, IEEE Transactions on Wireless Communications.

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

[12]  Andrea E. F. Clementi,et al.  Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks , 1999, RANDOM-APPROX.

[13]  Eytan Modiano,et al.  Minimum energy disjoint path routing in wireless ad-hoc networks , 2003, MobiCom '03.

[14]  Andrea E. F. Clementi,et al.  The Power Range Assignment Problem in Radio Networks on the Plane , 2000, STACS.

[15]  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).

[16]  Hanan Shpungin,et al.  Fault-tolerant power assignment and backbone in wireless networks , 2006, Fourth Annual IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOMW'06).

[17]  Hanan Shpungin,et al.  On construction of minimum energy k-fault resistant topologies , 2009, Ad Hoc Networks.

[18]  Andrea E. F. Clementi,et al.  Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks , 2004, STACS.

[19]  Mauro Leoncini,et al.  On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks , 2002, IFIP TCS.

[20]  Santosh S. Vempala,et al.  Approximation algorithms for minimum-cost k-vertex connected subgraphs , 2002, STOC '02.

[21]  Afonso Ferreira,et al.  The Minimum Range Assignment Problem on Linear Radio Networks , 2002, Algorithmica.

[22]  Ion I. Mandoiu,et al.  Symmetric Connectivity with Minimum Power Consumption in Radio Networks , 2002, IFIP TCS.

[23]  Gruia Calinescu,et al.  Bounded-hops power assignment in ad-hoc wireless networks , 2004, 2004 IEEE Wireless Communications and Networking Conference (IEEE Cat. No.04TH8733).

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

[25]  Ashish Goel,et al.  Energy-Efficient Broadcasting in Wireless ad hoc Networks Lower Bounds and Algorithms , 2002, J. Interconnect. Networks.

[26]  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).

[27]  Christoph Amb.  An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks , 2005 .

[28]  B. R. Badrinath,et al.  On the node-scheduling approach to topology control in ad hoc networks , 2005, MobiHoc '05.

[29]  Stefan Funke,et al.  Bounded-Hop Energy-Efficient Broadcast in Low-Dimensional Metrics Via Coresets , 2007, STACS.

[30]  Peter Sanders,et al.  Energy Optimal Routing in Radio Networks Using Geometric Data Structures , 2002, ICALP.

[31]  Vahab S. Mirrokni,et al.  Power Optimization for Connectivity Problems , 2005, IPCO.

[32]  Peng-Jun Wan,et al.  Range Assignment for High Connectivity in Wireless Ad Hoc Networks , 2003, ADHOC-NOW.

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

[34]  Ivan Stojmenovic,et al.  Localized minimum-energy broadcasting in ad-hoc networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[35]  Jean-Pierre Hubaux,et al.  Minimum-energy broadcast in all-wireless networks: NP-completeness and distribution issues , 2002, MobiCom '02.

[36]  Madhav V. Marathe,et al.  Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks , 2002, MobiHoc '02.

[37]  Nicole Immorlica,et al.  Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks , 2007, IEEE/ACM Trans. Netw..

[38]  Hanan Shpungin,et al.  k-fault resistance in wireless ad-hoc networks , 2005, DIALM-POMC '05.

[39]  Bhaskar Krishnamachari,et al.  Minimum latency joint scheduling and routing in wireless sensor networks , 2007, Ad Hoc Networks.

[40]  Stéphane Pérennes,et al.  Improved Approximation Results for the Minimum Energy Broadcasting Problem , 2004, DIALM-POMC '04.

[41]  Andrea E. F. Clementi,et al.  Energy Consumption in Radio Networks: Selfish Agents and Rewarding Mechanisms , 2003, SIROCCO.