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Degree-Bounded Planar Spanner with Low Weight

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  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2005; Song, Li, Wang

Problem Definition

An important requirement of wireless ad hoc networks is that they should be self‐organizing, and transmission ranges and data paths may need to be dynamically restructured with changing topology. Energy conservation and network performance are probably the most critical issues in wireless ad hoc networks, because wireless devices are usually powered by batteries only and have limited computing capability and memory. Hence, in such a dynamic and resource‐limited environment, each wireless node needs to locally select communication neighbors and adjust its transmission power accordingly, such that all nodes together self-form a topology that is energy efficient for both unicast and broadcast communications.

To support energy‐efficient unicast, the topology is preferred to have the following features in the literature:

  1. 1.

    Power Spanner: [1, 9, 13, 16, 17] Formally speaking, a subgraph H is called a power...

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Recommended Reading

  1. Bose P, Gudmundsson J, Smid M (2002) Constructing plane spanners of bounded degree and low weight. In: Proceedings of European symposium of algorithms, University of Rome, 17–21 Sept 2002

    Google Scholar 

  2. Bose P, Morin P, Stojmenovic I, Urrutia J (2001) Routing with guaranteed delivery in ad hoc wireless networks. ACM/Kluwer Wirel Netw 7(6):609–616, 3rd international workshop on discrete algorithms and methods for mobile computing and communications, pp 48–55 (1999)

    Article  MATH  Google Scholar 

  3. Burkhart M, von Rickenbach P, Wattenhofer R, Zollinger A (2004) Does topology control reduce interference. In: ACM international symposium on mobile Ad-Hoc networking and computing (Mobi-Hoc), Tokyo, 24–26 May 2004

    Google Scholar 

  4. Gabriel KR, Sokal RR (1969) A new statistical approach to geographic variation analysis. Syst Zool 18:259–278

    Article  Google Scholar 

  5. Karp B, Kung HT (2000) Gpsr: greedy perimeter stateless routing for wireless networks. In: Proceedings of the ACM/IEEE international conference on mobile computing and networking (MobiCom), Boston, 6–11 Aug 2000

    Google Scholar 

  6. Kleinrock L, Silvester J (1978) Optimum transmission radii for packet radio networks or why six is a magic number. In: Proceedings of the IEEE national telecommunications conference, Birmingham, pp 431–435, 4–6 Dec 1978

    Google Scholar 

  7. Kuhn F, Wattenhofer R, Zollinger A (2002) Asymptotically optimal geometric mobile ad-hoc routing. In: International workshop on discrete algorithms and methods for mobile computing and communications (DIALM), Atlanta, 28 Sept 2002

    Google Scholar 

  8. Kuhn F, Wattenhofer R, Zollinger A (2003) Worst-case optimal and average-case efficient geometric ad-hoc routing. In: ACM international symposium on mobile Ad-Hoc networking and computing (MobiHoc), Anapolis, 1–3 June 2003

    Google Scholar 

  9. Li L, Halpern JY, Bahl P, Wang Y-M, Wattenhofer R (2001) Analysis of a cone-based distributed topology control algorithms for wireless multi-hop networks. In: PODC: ACM symposium on principle of distributed computing, Newport, 26–29 Aug 2001

    Google Scholar 

  10. Li X-Y (2003) Approximate MST for UDG locally. In: COCOON, Big Sky, 25–28 July 2003

    Google Scholar 

  11. Li X-Y, Wan P-J, Wang Y, Frieder O (2002) Sparse power efficient topology for wireless networks. In: IEEE Hawaii international conference on system sciences (HICSS), Big Island, 7–10 Jan 2002

    Google Scholar 

  12. Li X-Y, Wang Y, Song W-Z, Wan P-J, Frieder O (2004) Localized minimum spanning tree and its applications in wireless ad hoc networks. In: IEEE INFOCOM, Hong Kong, 7–11 Mar 2004

    Google Scholar 

  13. Song W-Z, Wang Y, Li X-Y, Frieder O (2004) Localized algorithms for energy efficient topology in wireless ad hoc networks. In: ACM international symposium on mobile Ad-Hoc networking and computing (MobiHoc), Tokyo, 24–26 May 2004

    Google Scholar 

  14. Toussaint GT (1980) The relative neighborhood graph of a finite planar set. Pattern Recognit 12(4):261–268

    Article  MathSciNet  MATH  Google Scholar 

  15. Wan P-J, Calinescu G, Li X-Y, Frieder O (2001) Minimum-energy broadcast routing in static ad hoc wireless networks. ACM wireless networks (2002), To appear, Preliminary version appeared in IEEE INFOCOM, Anchorage, 22–26 Apr 2001

    Google Scholar 

  16. Wang Y, Li X-Y (2003) Efficient construction of bounded degree and planar spanner for wireless networks. In: ACM DIALMPOMC joint workshop on foundations of mobile computing, San Diego, 19 Sept 2003

    Google Scholar 

  17. Yao AC-C (1982) On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM J Comput 11:721–736

    Article  MathSciNet  MATH  Google Scholar 

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Song, WZ., Li, XY., Wang, W. (2016). Degree-Bounded Planar Spanner with Low Weight. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_103

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