Skip to main content
SpringerLink
Log in

Minimum power assignment in wireless ad hoc networks with spanner property

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Power assignment for wireless ad hoc networks is to assign a power for each wireless node such that the induced communication graph has some required properties. Recently research efforts have focused on finding the minimum power assignment to guarantee the connectivity or fault-tolerance of the network. In this paper, we study a new problem of finding the power assignment such that the induced communication graph is a spanner for the original communication graph when all nodes have the maximum power. Here, a spanner means that the length of the shortest path in the induced communication graph is at most a constant times of the length of the shortest path in the original communication graph. Polynomial time algorithm is given to minimize the maximum assigned power with spanner property. The algorithm also works for any other property that can be tested in polynomial time and is monotone. We then give a polynomial time approximation method to minimize the total transmission radius of all nodes. Finally, we propose two heuristics and conduct extensive simulations to study their performance when we aim to minimize the total assigned power of all nodes.

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.

Similar content being viewed by others

References

  • Althaus E, Călinescu G, Mandoiu I, Prasad S, Tchervenski N, Zelikovsly A (2003) Power efficient range assignment in ad-hoc wireless networks, to appear in Wireless Networks, preliminary results in: IEEE Wireless Communications and Networking Conference (WCNC03)

  • Arya S, Das G, Mount D, Salowe J, Smid M (1995) Euclidean spanners: Short, thin, and lanky. In: Proc. 27th ACM STOC, pp 489–498

  • Blough D, Leoncini M, Resta G, Santi P (2002) On the symmetric range assignment problem in wireless ad hoc networks. In: Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science (TCS)

  • Călinescu G, Kapoor S, Olshevsky A, Zelikovsky A (2003) Network lifetime and power assignment in ad-hoc wireless networks. In: Proc. 11th Ann. European Symp. on Algorithms (ESA 2003)

  • Călinescu G, Wan PJ (2003) Range assignment for high connectivitity in wireless ad hoc networks, to appear in Mobile Networks and Applications (MONET), preliminary version In: 2nd International Conf. on AD-HOC Networks and Wireless (AdHoc-Now)

  • Chen WT, Huang N.-F. (1989) The strongly connecting problem on multihop packet radio networks. IEEE Transactions on Communications 37(3):293–295

    Google Scholar 

  • Cheriyan J, Vempala S, Vetta A (2002) Approximation algorithms for minimum-cost k-vertex connected subgraphs. In: Proc. of the 34th annual ACM symposium on Theory of computing

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

  • Clementi AEF, Penna P, Silvestri R (2000b) On the power assignment problem in radio networks, Electronic Colloquium on Computational Complexity (ECCC) (054)

  • Clementi AEF, Ferreira A, Penna P, Perennes S, Silvestri R (2000c) The minimum range assignment problem on linear radio networks. In: European Symposium on Algorithms, pp 143–154

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

  • Clementi AE, Huiban G, Penna P, Rossi G, Verhoeven YC (2002) Some recent theoretical advances and open questions on energy consumption in ad-hoc wireless networks. In: 3rd Workshop on Approximation and Randomization Algorithms in Communication Networks

  • Czumaj A, Zhao H (2003) Fault-tolerant geometric spanners, In: Proceedings of the 19th conference on Computational geometry. ACM Press, pp 1–10

  • Gabriel K, Sokal R (1969) A new statistical approach to geographic variation analysis. Systematic Zoology 18: 259–278

    Google Scholar 

  • Gudmundsson J, Levcopoulos C, Narasimhan G (2000) Improved greedy algorithms for constructing sparse geometric spanners. In: Scandinavian Workshop on Algorithm Theory, pp 314–327

  • Hajiaghayi M, Immorlica N, Mirrokni VS (2003) Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks. In: Proc. of the 9th annual international conference on Mobile computing and networking, pp 300–312

  • Huiban G, Verhoeven YC (2004) A self-stabilized distributed algorithm for the range assignment in ad-hoc wireless networks, Soumis à Parallel Processing Letters

  • Kirousis LM, Kranakis E, Krizanc D, Pelc A (2000) Power consumption in packet radio networks. Theoretical Computer Science 243(1–2): 289–305

    MathSciNet  Google Scholar 

  • Krumke SO, Liu R, Lloyd EL, Marathe MV, Ramanathan R, Ravi SS (2003) Topology control problems under symmetric and asymmetric power thresholds. In: ADHOC-NOW 2003, pp. 187–198

  • Li Y, Thai MT, Wang F, Du D-Z (2005) On the construction of a strongly connected broadcast arborescence with bounded transmission delay, accepted by IEEE Trans. on Mobile Computing

  • Li X-Y, Wan P.-J, Wang Y (2001) Power efficient and sparse spanner for wireless ad hoc networks, In: IEEE Int. Conf. on Computer Communications and Networks

  • Li X-Y, Wang Y (2004) Efficient construction of bounded degree planar spanner, International Journal of Computational Geometry and Applications 14(1/2) 69–84

    MathSciNet  Google Scholar 

  • Lloyd EL, Liu R, Marathe MV, Ramanathan R, Ravi SS (2002) Algorithmic aspects of topology control problems for ad hoc networks. In: Proc. of the 3rd ACM international symposium on Mobile ad hoc networking & computing

  • Ramanathan R, Hain R (2000) Topology control of multihop wireless networks using transmit power adjustment. In: IEEE INFOCOM (2), pp. 404–413

  • Srinivas A, Modiano E (2003) Minimum energy disjoint path routing in wireless ad-hoc networks. In: Proceedings of the 9th annual international conference on Mobile computing and networking, pp 122–133

  • Wan PJ, Calinescu G, Li X-Y, Frieder O, (2002) Minimum-energy broadcast routing in static ad hoc wireless networks, ACM Wireless Networks 8(6):607–617

    Google Scholar 

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

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Yu Wang

  2. Department of Computer Science, Illinois Institute of Technology, Chicago, IL, 60616, USA

    Xiang-Yang Li

Authors
  1. Yu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiang-Yang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Wang.

Additional information

The author is partially supported by NSF CCR-0311174.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Y., Li, XY. Minimum power assignment in wireless ad hoc networks with spanner property. J Comb Optim 11, 99–112 (2006). https://doi.org/10.1007/s10878-006-5980-0

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-006-5980-0

Keywords

Search

Navigation