Localized Construction of Low Weighted Structure and Its Applications in Wireless Ad Hoc Networks

We consider a wireless network composed of a set of n wireless nodes distributed in a two dimensional plane. The signal sent by every node can be received by all nodes within its transmission range, which is uniform and normalized to one unit. We present the first distributed method to construct a bounded degree planar connected structure LRNG, whose total link length is within a constant factor of the minimum spanning tree using total O(n) messages under the broadcast communication model. Moreover, in our method, every node only uses its two-hop information to construct such structure, i.e., it is localized method. We show that some two-hop information is necessary to construct any low-weighted structure. We also study the application of this structure in efficient broadcasting in wireless ad hoc networks. We prove that, for broadcasting, the relative neighborhood graph (RNG), which is the previously best-known sparse structure that can be constructed locally, could use energy O(n) times the total energy used by our structure LRNG. Our simulations show that the broadcasting based on LRNG consumes energy about 36% more than that by MST, and broadcasting based on RNG consumes energy about 64% more than that by MST. We also show that no localized method can construct a structure for broadcasting with total power consumption asymptotically better than LRNG.

[1]  RNG and internal node based broadcasting algorithms for wireless one-to-one networks , 2001, MOCO.

[2]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

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

[4]  Xiang-Yang Li,et al.  Efficient Construction of Low Weight Bounded Degree Planar Spanner , 2003, COCOON.

[5]  Vahab S. Mirrokni,et al.  Fault-Tolerant and 3-Dimensional Distributed Topology Control Algorithms in Wireless Multi-hop Networks , 2006, Wirel. Networks.

[6]  Xiang-Yang Li,et al.  Geometric spanners for wireless ad hoc networks , 2002, Proceedings 22nd International Conference on Distributed Computing Systems.

[7]  Ram Ramanathan,et al.  Topology control of multihop wireless networks using transmit power adjustment , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

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

[10]  David Simplot,et al.  Localized energy efficient broadcast for wireless networks with directional antennas , 2002 .

[11]  Paramvir Bahl,et al.  Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks , 2001, PODC '01.

[12]  Xiang-Yang Li,et al.  Minimum-Energy Broadcasting in Static Ad Hoc Wireless Networks , 2002, Wirel. Networks.

[13]  Michalis Faloutsos.  Creating Optimal Distributed Algorithms for Minimum Spanning Trees , 1995 .

[14]  Xiang-Yang Li,et al.  Distributed spanner with bounded degree for wireless ad hoc networks , 2002, Proceedings 16th International Parallel and Distributed Processing Symposium.

[15]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[16]  Ivan Stojmenovic,et al.  Routing with Guaranteed Delivery in Ad Hoc Wireless Networks , 1999, DIALM '99.

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

[18]  Xiang-Yang Li,et al.  Localized low-weight graph and its applications in wireless ad hoc networks , 2004, IEEE INFOCOM 2004.

[19]  Paramvir Bahl,et al.  Distributed Topology Control for Wireless Multihop Ad-hoc Networks , 2001, INFOCOM.

[20]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[21]  Anthony Ephremides,et al.  On the construction of 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).

[22]  Yu-Chee Tseng,et al.  Energy-Efficient Topology Control for Wireless Ad Hoc Sensor Networks , 2004, J. Inf. Sci. Eng..

[23]  Shay Kutten,et al.  A sub-linear time distributed algorithm for minimum-weight spanning trees , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[24]  Giri Narasimhan,et al.  A new way to weigh Malnourished Euclidean graphs , 1995, SODA '95.

[25]  Rajmohan Rajaraman,et al.  Topology control and routing in ad hoc networks: a survey , 2002, SIGA.

[26]  Xiang Li,et al.  Lo-calized minimum spanning tree and its applications in wireless ad hoc networks , 2004, INFOCOM 2004.

[27]  Xiang-Yang Li,et al.  Localized Construction of Bounded Degree and Planar Spanner for Wireless Ad Hoc Networks , 2003, DIALM-POMC '03.

[28]  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).

[29]  Pierre A. Humblet,et al.  A Distributed Algorithm for Minimum-Weight Spanning Trees , 1983, TOPL.

[30]  Lui Sha,et al.  Design and analysis of an MST-based topology control algorithm , 2003, IEEE Transactions on Wireless Communications.

[31]  Xiang-Yang Li,et al.  Applications of k-local MST for topology control and broadcasting in wireless ad hoc networks , 2004, IEEE Transactions on Parallel and Distributed Systems.

[32]  Brad Karp,et al.  GPSR: greedy perimeter stateless routing for wireless networks , 2000, MobiCom '00.

[33]  Tamás Lukovszki,et al.  Distributed Maintenance of Resource Efficient Wireless Network Topologies (Distinguished Paper) , 2002, Euro-Par.

[34]  Li Li,et al.  Distributed topology control for power efficient operation in multihop wireless ad hoc networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[35]  Michalis Faloutsos,et al.  Optimal distributed algorithm for minimum spanning trees revisited , 1995, PODC '95.

[36]  Limin Hu,et al.  Topology control for multihop packet radio networks , 1993, IEEE Trans. Commun..

[37]  YU WANG,et al.  Distributed Spanners with Bounded Degree for Wireless Ad Hoc Networks , 2003, Int. J. Found. Comput. Sci..

[38]  Madhav V. Marathe,et al.  Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks , 2005, Mob. Networks Appl..

[39]  Xiang-Yang Li,et al.  Distributed construction of a planar spanner and routing for ad hoc wireless networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[40]  Xiang-Yang Li,et al.  Sparse power efficient topology for wireless networks , 2002, Proceedings of the 35th Annual Hawaii International Conference on System Sciences.