Skip to main content
SpringerLink
Log in

Cover-Free Families and Topology-Transparent Scheduling for MANETs

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

We examine the combinatorial requirements of topology-transparent transmission schedules in a mobile ad hoc network (MANET). Specifically, if each of the N nodes has at most D active neighbors, we require the schedule to guarantee a collision-free transmission to each neighbor. This requirement is met by a cover-free family. We show that existing constructions for topology-transparent schedules correspond to an orthogonal array. Moreover, we show that Steiner systems support the largest number of nodes for a given schedule length. Both of these combinatorial objects are special cases of cover-free families. Analytically and numerically, we examine slot guarantees, expected throughput, and normalized expected throughput for systems of small strength, exploring the sensitivity of the response to D. Expected throughput provides a better performance metric than the minimum throughput results obtained earlier. The impact of a more realistic model of acknowledgments is also examined. The extension of the schedule to multiple frames returns us to the orthogonal arrays. The very density of Steiner systems that afforded an improvement over orthogonal arrays in one frame impedes the best extension to more frames.

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

  1. IEEE Standard 802.11: Wireless LAN Medium Access Control and Physical Layer Specifications, December (1999).

  2. R. J. R. Abel, F. E. Bennett and G. Ge, The existence of four HMOLS with equal sized holes, Des. Codes Crypt., Vol. 26 (2002) pp. 7–31.

    Google Scholar 

  3. R. J. R. Abel and A. C. H. Ling, Some new constructions for (v, 5, w*, 1) PBDs, J. Combin. Math. Combin. Comput., Vol. 32 (2000) pp. 97–102.

    Google Scholar 

  4. F. E. Bennett, C. J. Colbourn and R. C. Mullin, Quintessential pairwise balanced designs, J. Stat. Plann. Infer., Vol. 72 (1998) pp. 15–66.

    Google Scholar 

  5. M. Benveniste, G. Chesson, M. Hoeben, A. Singla, H. Teunissen and M. Wentink, Enhanced distributed coordination function (EDCF), In IEEE Working Document 802.11–01/131r1, March (2001).

  6. I. Chlamtac and A. Faragó, Making transmission schedules immune to topology changes in multihop packet radio networks, IEEE/ACM Transactions on Networking, Vol. 2, No. 1, February (1994) pp. 23–29.

    Google Scholar 

  7. I. Chlamtac, A. Faragó and H. Zhang, Time-spread multiple-access (TSMA) protocols for multihop mobile radio networks, IEEE/ACM Transactions on Networking, Vol. 5, No. 6, December (1997) pp. 804–812.

    Google Scholar 

  8. I. Chlamtac and S. Pinter, Distributed node organization algorithm for channel access in a multi-hop packet radio network, IEEE Transactions on Computers, Vol. 36, No. 6 (1987) pp. 728–737.

    Google Scholar 

  9. C. J. Colbourn and J. H. Dinitz, (eds), The CRC Handbook of Combinatorial Designs, CRC Press, Inc., Boca Raton, FL (1996).

    Google Scholar 

  10. C. J. Colbourn, J. H. Dinitz and D. R. Stinson, Applications of combinatorial designs to communications, cryptography, and networking. In J. D. Lamb and D. A. Preece (eds.), Surveys in Combinatorics, 1999, London Mathematical Society, Lecture Note Series 267, Cambridge University Press (1999) pp. 37–100.

  11. C. J. Colbourn, V. R. Syrotiuk and A. C. H. Ling, Steiner systems for topology-transparent access control in MANETs. In Proceedings of the Second International Conference on Ad Hoc Networks and Wireless (AdHoc Now'03), Montreal, Quebec (2003) pp. 247–258.

  12. D.-Z. Du and F. K. Hwang, Combinatorial Group Testing and its Applications, World Scientific Publishing Co. Pte. Ltd., second edition (2000).

  13. A. D'yachkov, V. Rykov and A. M. Rashad, Superimposed distance codes, Problems Control and Information Theory, Vol. 18 (1989) pp. 237–250.

    Google Scholar 

  14. P. Erdös, P. Frankl and Z. Füredi, Families of finite sets in which no set is covered by the union of r others, Israel J. Math., Vol. 51 (1985) pp. 79–89.

    Google Scholar 

  15. A. S. Hedayat, N. J. A. Sloane and J. Stufken, Orthogonal Arrays, Theory and Applications, Springer-Verlag, Inc., New York, NY (1999).

    Google Scholar 

  16. J.-H. Ju and V. O. K. Li, An optimal topology-transparent scheduling method in multihop packet radio networks, IEEE/ACM Transactions on Networking, Vol. 6, No. 3, June (1998) pp. 298–306.

    Google Scholar 

  17. A. D. Myers, V. R. Syrotiuk and G. Záruba, An adaptive generalized transmission protocol for mobile ad hoc networks, ACM/Kluwer Journal on Mobile Networks and Applications (MONET), Vol. 7 (2002) pp. 493–502.

    Google Scholar 

  18. L. Romdhani, Q. Ni and T. Turletti, AEDCF: Enhanced service differentiation for IEEE 802.11 wireless ad-hoc networks, Technical Report 4544, INRIA (2002).

  19. M. Ruszinkó, On the upper bound of the size of the r-cover-free families, Journal of Combinatorial Theory, Series A, Vol. 66 (1994) pp. 302–310.

    Google Scholar 

  20. J. L. Sobrinho and A. S. Krishnakumar, Quality-of-service in ad hoc carrier sense multiple access wireless networks, IEEE Journal on Selected Areas in Communications, Vol. 17, No. 8, August (1999) pp. 1352–1368.

    Google Scholar 

  21. D. R. Stinson, R. Wei and L. Zhu, Some new bounds for cover-free families, Journal of Combinatorial Theory, Series A, Vol. 90 (2000) pp. 224–234.

    Google Scholar 

  22. V. R. Syrotiuk, C. J. Colbourn and A. C. H. Ling, Topology-transparent scheduling in MANETs using orthogonal arrays, In Proceedings of the DIALM-POMC Joint Workshop on Foundations of Mobile Computing, San Diego, CA (2003) pp. 43–49.

  23. V. R. Syrotiuk, Wireless medium access control protocols, In (A. Boukerche and I. Chlamtac, eds.), Handbook on Algorithmic Aspects of Wireless Networks, CRC Press, (to appear).

  24. Waterloo Maple Inc., Maple 8. http://www.maplesoft.com/main.html

  25. R. Zheng, C.-J. Hou and L. Sha, Asynchronous wakeup for ad hoc networks, Proceedings of the Fourth International Conference on Mobile Ad Hoc Networking & Computing (Mobihoc03), Annapolis, MD, June 1–3 (2003) pp.35–45.

  26. C. Zhu and S. Corson, A five-phase reservation protocol (FPRP) for mobile ad hoc networks, In Proceedings of 17th Annual Joint Conference of the IEEE Computer and Communication Societies (INFOCOM'98), San Francisco, CA, March 29–April 2 (1998) pp. 315–321.

Download references

Author information

Authors and Affiliations

  1. Computer Science and Engineering, Arizona State University, Tempe, AZ, 85287-8809, U.S.A.

    Charles J. Colbourn & Violet R. Syrotiuk

  2. Computer Science, University of Vermont, Burlington, VT, 05405, U.S.A.

    Alan C. H. Ling

Authors
  1. Charles J. Colbourn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan C. H. Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Violet R. Syrotiuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colbourn, C.J., Ling, A.C.H. & Syrotiuk, V.R. Cover-Free Families and Topology-Transparent Scheduling for MANETs. Designs, Codes and Cryptography 32, 65–95 (2004). https://doi.org/10.1023/B:DESI.0000029213.74879.e0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:DESI.0000029213.74879.e0

Search

Navigation