Skip to main content

Advertisement

SpringerLink
Log in

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

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • M. Bahramgiri, M.T. Hajiaghayi and V.S. Mirrokni, Fault-tolerant and 3-dimensional distributed topology control algorithms in wireless multi-hop networks, in: Proceedings of the 11th Annual IEEE Internation Conference on Computer Communications and Networks (ICCCN) (2002), pp. 392–397.

  • P. Bose, P. Morin, I. Stojmenovic and J. Urrutia, Routing with guaranteed delivery in ad hoc wireless networks, in: ACM/Kluwer Wireless Networks, 7(6) (2001) 609–616, 3rd int. Workshop on Discrete Algorithms and methods for mobile computing and communications, (1999) 48–55.

  • J. Cartigny, D. Simplot and I. Stojmenovic, Localized energy efficient broadcast for wireless networks with directional antennas, in: Proc. IFIP Mediterranean Ad Hoc Networking Workshop (MED-HOC-NET 2002), Sardegna, Italy (2002).

  • V. Chvátal, A greedy heuristic for the set-covering problem, Mathematics of Operations Research 4(3) (1979) 233–235.

  • A. Clementi, P. Crescenzi, P. Penna, G. Rossi and P. Vocca, On the complexity of computing minimum energy consumption broadcast subgraphs, in: 18th Annual Symposium on Theoretical Aspects of Computer Science, LNCS 2010 (2001) pp. 121–131.

  • A. Clementi, P. Penna and R. Silvestri, The power range assignment problem in radio networks on the plane, in: XVII Symposium on Theoretical Aspects of Computer Science (STACS'00), LNCS(1770) (2000) pp. 651–660.

  • A. Clementi, P. Penna and R. Silvestri, On the power assignment problem in radio networks, in: Electronic Colloquium on Computational Complexity (2001), To approach. Preliminary results in APPROX'99 and STACS'2000.

  • T.J. Cormen, C.E. Leiserson and R.L. Rivest, Introduction to Algorithms (MIT Press and McGraw-Hill, 1990).

  • G. Das, G. Narasimhan and J. Salowe, A new way to weigh malnourished euclidean graphs, in: ACM Symposium of Discrete Algorithms (1995) pp. 215–222.

  • M. Faloutsos and M. Molle, Creating optimal distributed algorithms for minimum spanning trees, Tech. Rep. Technical Report CSRI-327 (also submitted in WDAG '95) (1995).

  • R. Gallager, P. Humblet and P. Spira, A distributed algorithm for minimumweight spanning trees, ACM Transactions on Programming Languages and Systems 5(1) (1983) 66–77.

    Article  Google Scholar 

  • J.A. Garay, S. Kutten and D. Peleg, A sub-linear time distributed algorithms for minimum-weight spanning trees, in: Symp. on Theory of Computing (1993) pp. 659–668.

  • M. Grünewald, T. Lukovszki, C. Schindelhauer and K. Volbert, Distributed maintenance of resource efficient wireless network topologies, (2002), submitted for publication.

  • L. Hu, Topology control for multihop packet radio networks, IEEE Trans. Communications 41(10) (1993).

  • B. Karp and H.T. Kung, Gpsr: Greedy perimeter stateless routing for wireless networks, in: ACM/IEEE International Conference on Mobile Computing and Networking (2000).

  • L.M. Kirousis, E. Kranakis, D. Krizanc and A. Pelc, Power consumption in packet radio networks, Theoretical Computer Science 243 (2000) 289–305.

    Article  Google Scholar 

  • Xiang-Yang Li, G. Calinescu and Peng-Jun Wan, Distributed construction of planar spanner and routing for ad hoc wireless networks, in: 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM) (2002) vol. 3.

  • L. Li, J.Y. Halpern, P. Bahl, Yi-Min Wang and R. Wattenhofer, Analysis of a cone-based distributed topology control algorithms for wireless multi-hop networks, in: ACM Symposium on Principle of Distributed Computing (PODC) (2001).

  • Xiang-Yang Li, Peng-Jun Wan, Yu Wang and Ophir Frieder, Sparse power efficient topology for wireless networks, Journal of Parallel and Distributed Computing (2002), To appear. Preliminary version appeared in ICCCN 2001.

  • Xiang-Yang Li, Peng-Jun Wan, Yu Wang and Ophir Frieder, Sparse power efficient topology for wireless networks, in: IEEE Hawaii Int. Conf. on System Sciences (HICSS) (2002).

  • Xiang-Yang Li, Yu Wang and Wen-Zhan Song, Applications of k-local MST for topology control and broadcasting in wireless ad hoc networks, IEEE Transaction on Parallel and Distributed Systems 15(12) (2004) 1057–1069.

    Google Scholar 

  • Xiang-Yang Li, Yu Wang, Peng-Jun Wan, Wan-Zhen Song and Ophir Frieder, Localized low weight graph and its applications in wireless ad hoc networks, in: IEEE INFOCOM, (2004).

  • Ning Li, J.C. Hou and Lui Sha, Design and analysis of a mst-based topology control algorithm, in: Proc. of IEEE INFOCOM 2003 (2003).

  • Xiang-Yang Li and Yu Wang, Efficient construction of bounded degree planar spanner, in: COCOON'03 (2003).

  • L. Lloyd, R. Liu, M.V. Marathe, R. Ramanathan and S.S. Ravi, Algorithmic aspects of topology control problems for ad hoc networks, in: IEEE MOBIHOC (2002).

  • R. Rajaraman, Topology control and routing in ad hoc networks: A survey, SIGACT News 33 (2002) 60–73.

    Google Scholar 

  • R. Ramanathan and R. Rosales-Hain, Topology control of multihop wireless networks using transmit power adjustment, in: IEEE INFOCOM (2000).

  • M. Seddigh, J. Solano Gonzalez and I. Stojmenovic, Rng and internal node based broadcasting algorithms for wireless one-to-one networks, ACM Mobile Computing and Communications Review 5(2) (2002) 37–44.

    Google Scholar 

  • Y.-C. Tseng, Y.-N. Chang and B.-H. Tzeng, Energy-efficient topology control for wireless ad hoc sensor networks, in: Proc. Int. Conf. Parallel and Distributed Systems (ICPADS) (2002).

  • G.T. Toussaint, The relative neighborhood graph of a finite planar set, Pattern Recognition 12(4) (1980) 261–268.

    Google Scholar 

  • Peng-Jun Wan, G. Calinescu, Xiang-Yang Li and Ophir Frieder, Minimum-energy broadcast routing in static ad hoc wireless networks, in: IEEE Infocom (2001).

  • P.J. Wan, G. Calinescu, Xiang-Yang Li and Ophir Frieder, Minimum-energy broadcast routing in static ad hoc wireless networks, ACM Wireless Networks (2002), Preliminary version appeared in: IEEE INFOCOM (2000).

  • Yu Wang and Xiang-Yang Li, Distributed spanner with bounded degree for wireless ad hoc networks, in: International Parallel and Distributed Processing Symposium: Parallel and Distributed Computing Issues in Wireless networks and Mobile Computing (April 2002).

  • Yu Wang and Xiang-Yang Li, Geometric spanners for wireless ad hoc networks, in: Proc. of 22nd IEEE International Conference on Distributed Computing Systems (ICDCS) (2002).

  • Yu Wang and Xiang-Yang Li, Localized construction of bounded degree planar spanner for wireless networks, in: ACM DialM-POMC (2003).

  • R. Wattenhofer, Li Li, P. Bahl and Yi-Min Wang, Distributed topology control for wireless multihop ad-hoc networks, in: IEEE INFOCOM'01 (2001).

  • J. Wieselthier, G. Nguyen and A. Ephremides, On the construction of energy-efficient broadcast and multicast trees in wireless networks, in: Proc. IEEE INFOCOM 2000 (2000) pp. 586–594.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Illinois Institute of Technology, 10 W. 31st Street, Chicago, IL, 60616, USA

    Xiang-Yang Li

Authors
  1. Xiang-Yang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiang-Yang Li.

Additional information

Xiang-Yang Li has been an Assistant Professor of Computer Science at the Illinois Institute of Technology since 2000. He hold MS (2000) and PhD (2001) degree at Computer Science from University of Illinois at Urbana-Champaign. He received his Bachelor degree at Computer Science and Bachelor degree at Business Management respectively from Tsinghua University, P.R. China in 1995. His research interests span the computational geometry, wireless ad hoc networks, game theory, optical networks, and cryptography. He is a Member of the ACM and IEEE.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, XY. Localized Construction of Low Weighted Structure and Its Applications in Wireless Ad Hoc Networks. Wireless Netw 11, 697–708 (2005). https://doi.org/10.1007/s11276-005-3524-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-005-3524-7

Keywords

Search

Navigation