Low-Latency Broadcast Scheduling in Ad Hoc Networks

  • Scott C. -H. Huang
  • Peng-Jun Wan
  • Xiaohua Jia
  • Hongwei Du
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4138)

Abstract

Broadcast is a fundamental operation in wireless network, and naïve flooding is simply not practical. Previous results showed that although broadcast scheduling can achieve constant approximation ratios in respect of latency, the current state-of-the-art algorithm’s ratio is still overwhelmingly large (≈650). In this paper we present two basic broadcast scheduling algorithms that both achieve small ratios 51 and 24, while preserving low redundancy 1 and 4 (in terms of number of retransmissions a node has to make). Moreover, we also present a highly efficient algorithm whose latency is \(R+O(\sqrt{R}\log^{1.5}R)\) (where R is the network radius) and each node only has to transmit up to 5 times. This result, in a sense of approximation, is nearly optimal since \(O(\sqrt{R}\log^{1.5}R)\) is negligible when R is large. Moreover, R is itself a lower bound for latency, so the approximation ratio is nearly 1 and this algorithm is nearly optimal.

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References

  1. 1.
    Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. Journal of Computer and System Sciences 43(2), 290–298 (1991)CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: 3rd ACM international symposium on Mobile ad hoc networking & computing–MobiHoc 2002, pp. 157–164. ACM Press, New York (2002)CrossRefGoogle Scholar
  3. 3.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in multihop radio networks: An exponential gap between determinism and randomization. Journal of Computer and System Sciences 45(1), 104–126 (1992)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Basagni, S., Chlamtac, I., Bruschi, D.: A mobility-transparent deterministic broadcast mechanism for ad hoc networks. IEEE/ACM Transactions on Networking 7(6), 799–807 (1999)CrossRefGoogle Scholar
  5. 5.
    Bruschi, D., Del Pinto, M.: Lower bounds for the broadcast problem in mobile radio networks. Distributed Computing 10(3), 129–135 (1997)CrossRefGoogle Scholar
  6. 6.
    Cheng, X., Huang, X., Li, D., Du, D.: Polynomial time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Technical Report. To appear in NetworksGoogle Scholar
  7. 7.
    Chlamtac, I., Faragó, A.: Making transmission schedules immune to topology changes in multihop packet radio networks. IEEE/ACM Transactions Networking 2(1), 23–29 (1994)CrossRefGoogle Scholar
  8. 8.
    Chlamtac, I., Kutten, S.: On broadcasting in radio networks–problem analysis and protocol design. IEEE Transactions on Communications 33, 1240–1246 (1985)CrossRefMATHGoogle Scholar
  9. 9.
    Chlamtac, I., Weinstein, O.: The wave expansion approach to broadcasting in multihop radio networks. IEEE Transactions on Communications 39, 426–433 (1991)CrossRefGoogle Scholar
  10. 10.
    Chlebus, B.S., Ga̧sieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. In: Symposium on Discrete Algorithms, pp. 861–870 (2000)Google Scholar
  11. 11.
    Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Math. 86(1-3), 165–177 (1990)CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. In: ICC (1), pp. 376–380 (1997)Google Scholar
  13. 13.
    Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. In: ICC (1), pp. 376–380 (1997)Google Scholar
  14. 14.
    Elkin, M., Kortsarz, G.: Logarithmic inapproximability of the radio broadcast problem. Journal of Algorithms 52, 8–25 (2004)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Elkin, M., Kortsarz, G.: Polylogarithmic Inapproximability of the Radio Broadcast Problem. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 105–116. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Elkin, M., Kortsarz, G.: An improved algorithm for radio networks, 2005. An earlier version appeared in SODA 2005 (2005)Google Scholar
  17. 17.
    Gaber, I., Mansour, Y.: Centralized broadcast in multihop radio networks. Journal of Algorithms 46(1), 1–20 (2003)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Gandhi, R., Parthasarathy, S., Mishra, A.: Minimizing broadcast latency and redundancy in ad hoc networks. In: ACM MobiHoc 2003, pp. 222–232 (2003)Google Scholar
  19. 19.
    Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. In: European Symposium on Algorithms, pp. 179–193 (1996)Google Scholar
  20. 20.
    Ju, J.-H., Li, V.O.K.: An optimal topology-transparent scheduling method in multihop packet radio networks. IEEE/ACM Transactions on Networking 6(3), 298–306 (1998)CrossRefMATHGoogle Scholar
  21. 21.
    Kowalski, D.R., Pelc, A.: Centralized deterministic broadcasting in undirected multihop radio networks. In: 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems–APPROX-RANDOM 2004, pp. 171–182 (2004)Google Scholar
  22. 22.
    Kushilevitz, E., Mansour, Y.: An Ω(D log(N/D)) lower bound for broadcast in radio networks. SIAM Journal on Computing 27, 702–712 (1998)CrossRefMathSciNetMATHGoogle Scholar
  23. 23.
    Linial, N., Saks, M.: Decomposing graphs into regions of small diameter. In: 2nd annual ACM-SIAM symposium on Discreate algorithms-SODA 1991, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics, pp. 320–330 (1991)Google Scholar
  24. 24.
    Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)CrossRefMathSciNetMATHGoogle Scholar
  25. 25.
    Ni, S.-Y., Tseng, Y.-C., Chen, Y.-S., Sheu, J.-P.: The broadcast storm problem in a mobile ad hoc network. In: 5th annual ACM/IEEE international conference on Mobile computing and networking–MobiCom 1999, pp. 151–162. ACM Press, New York (1999)CrossRefGoogle Scholar
  26. 26.
    Ramanathan, S., Lloyd, E.L.: Scheduling algorithms for multihop radio networks. IEEE/ACM Transactions on Networking 1(2), 166–177 (1993)CrossRefGoogle Scholar
  27. 27.
    Sen, A., Huson, M.L.: A new model for scheduling packet radio networks. Wireless Networks 3(1), 71–82 (1997)CrossRefGoogle Scholar
  28. 28.
    Sheu, J.-P., Hung, P.-K., Hsu, C.-S.: Scheduling of broadcasts in multihop wireless networks. In: The handbook of ad hoc wireless networks, pp. 483–495. CRC Press, Inc., Boca Raton (2003)Google Scholar
  29. 29.
    Sivakumar, R., Das, B., Bharghavan, V.: Spine routing in ad hoc networks. Cluster Computing 1(2), 237–248 (1998)CrossRefGoogle Scholar
  30. 30.
    Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. Mobile Networks and Applications 9(2), 141–149 (2004)CrossRefGoogle Scholar
  31. 31.
    Wegner, G.: Über endliche kreispackungen in der ebene. Studia Scientiarium Mathematicarium Hungarica 21, 1–28 (1986)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Scott C. -H. Huang
    • 1
  • Peng-Jun Wan
    • 1
    • 2
  • Xiaohua Jia
    • 1
  • Hongwei Du
    • 1
  1. 1.City University of Hong Kong 
  2. 2.Illinois Institute of Technology 

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