Skip to main content
SpringerLink
Log in

Approximate MST for UDG Locally

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2697))

Included in the following conference series:

Abstract

We consider a wireless network composed of a set of n wireless nodes distributed in a two dimensional plane. The signal sent by a node can be received by all nodes within its transmission region, which is a unit disk centered at this node. The nodes together define a unit disk graph (UDG) with edge uv iff ∥uv∥ ≤ 1. We present the first localized method to construct a bounded degree planar connected structure for UDG whose total edge length is within a constant factor of the minimum spanning tree. The total communication cost of our method is O(n), and every node only uses its two-hop information to construct such structure. 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 this structure uses only O(1/n) of the total energy of the previously best-known light weighted structure RNG.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Li, X.Y., Calinescu, G., Wan, P.J.: 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). Volume 3. (2002)

    Google Scholar 

  2. Li, X.Y., Wan, P.J., Wang, Y., Frieder, O.: Sparse power efficient topology for wireless networks. Journal of Parallel and Distributed Computing (2002) To appear. Preliminary version appeared in ICCCN 2001.

    Google Scholar 

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

    Google Scholar 

  4. Wang, Y., Li, X.Y.: Geometric spanners for wireless ad hoc networks. In: Proc. of 22nd IEEE International Conference on Distributed Computing Systems (ICDCS). (2002)

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  7. Li, X.Y., Wang, Y.: Localized construction of bounded degree planar spanner for wireless networks (2003) Submitted for publication.

    Google Scholar 

  8. Wan, P.J., Calinescu, G., Li, X.Y., Frieder, O.: Minimum-energy broadcast routing in static ad hoc wireless networks. ACM Wireless Networks (2002) Preliminary version appeared in IEEE INFOCOM 2000.

    Google Scholar 

  9. Faloutsos, M., Molle, M.: Creating optimal distributed algorithms for minimum spanning trees. Technical Report Technical Report CSRI-327 (also submitted in WDAG’ 95) (1995)

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  14. Li, X.Y., Wan, P.J., Wang, Y., Frieder, O.: Sparse power efficient topology for wireless networks. In: IEEE Hawaii Int. Conf. on System Sciences (HICSS). (2002)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  17. Clementi, A., Crescenzi, P., Penna, P., Rossi, G., Vocca, P.: On the complexity of computing minimum energy consumption broadcast subgraphs. In: 18th Annual Symposium on Theoretical Aspects of Computer Science, LNCS 2010. (2001)

    Google Scholar 

  18. Li, X.Y., Wang, Y.: Efficient construction of low weight bounded degree planar spanner (2003). COCOON 2003.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Illinois Institute of Technology, 10W. 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

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, One University Station, C0500, Austin, TX, 78712, USA

    Tandy Warnow

  2. Department of Computer Science, Montana State University, EPS 357, Bozeman, MT, 59717, USA

    Binhai Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, XY. (2003). Approximate MST for UDG Locally. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_37

Download citation

  • DOI: https://doi.org/10.1007/3-540-45071-8_37

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40534-4

  • Online ISBN: 978-3-540-45071-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation