Skip to main content

Efficient Constructions of Generalized Superimposed Codes with Applications to Group Testing and Conflict Resolution in Multiple Access Channels

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

Abstract

In this paper we introduce a parameterized generalization of the well known superimposed codes. We give algorithms for their constructions and we provide non-existential results. We apply our new combinatorial structures to the efficient solution of new group testing problems and access coordination issues in multiple access channels.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Barillot, B. Lacroix, and D. Cohen, “Theoretical analysis of library screening using an n-dimensional pooling strategy”, Nucleic Acids Research, 6241–6247, 1991.

    Google Scholar 

  2. D. J. Balding, W. J. Bruno, E. Knill, and D.C. Torney, “A comparative survey of non-adaptive pooling design” in: Genetic mapping and DNA sequencing, IMA Volumes in Mathematics and its Applications, Springer-Verlag, 133–154, 1996.

    Google Scholar 

  3. D. Bertsekas and R. Gallager, Data Networks, Prentice Hall, 1992.

    Google Scholar 

  4. W. J. Bruno, D. J. Balding, E. Knill, D. Bruce, C. Whittaker, N. Dogget, R. Stalling, and D.C. Torney, “Design of efficient pooling experiments”, Genomics, 26, 21–30, 1995.

    Article  Google Scholar 

  5. G. Caire, E. Leonardi, and E. Viterbo, “Modulation and coding for the Gaussian collision channel”, IEEE Trans on Inform. Theory, 46, No. 6, 2007–2026, 2000.

    Article  MATH  Google Scholar 

  6. S.C. Chang and E. J. Weldon, “Coding for t-user multiple-access channels”, IEEE Trans. on Inform. Theory, 25, 684–691, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Chaudhuri and J. Radhakrishnan, “Deterministic restrictions in circuit complexity”, STOC 96, 30–36.

    Google Scholar 

  8. R.W. Chen and F. K. Hwang, “K-definite group testing and its application to polling in computer networks”, Congressus Numerantium, 47, 145–149, 1985.

    MathSciNet  Google Scholar 

  9. B. S. Chlebus, “Randomized communication in radio networks”, in: Handbook of Randomized Computing, Kluwer Academic Publishers, vol. I, 401–456, 2001.

    MathSciNet  Google Scholar 

  10. B. Chor, A. Fiat, and M. Naor, “Tracing traitors”, Crypto 94, LNCS, 839, Springer-Verlag, Berlin, 257–270, 1994.

    Google Scholar 

  11. A. E. F. Clementi, A. Monti and R. Silvestri, “Selective families, superimposed codes, and broadcasting on unknown radio networks”, SODA 01, 709–718.

    Google Scholar 

  12. P. Damaschke, “Randomized group testing for mutually obscuring defectives”, Information Processing Letters, 67, 131–5, 1998.

    Article  MathSciNet  Google Scholar 

  13. A. De Bonis and U. Vaccaro, “Improved algorithms for group testing with inhibitors”, Information Processing Letters, 67, 57–64, 1998.

    Article  MathSciNet  Google Scholar 

  14. R. Dorfman, “The detection of defective members of large populations”, Ann. Math. Statist., 14, 436–440, 1943.

    Article  Google Scholar 

  15. D. Z. Du and F.K. Hwang, Combinatorial Group Testing and its Applications, World Scientific, 2nd edition, 2000.

    Google Scholar 

  16. A.G. Dyachkov, V.V. Rykov, “A survey of superimposed code theory”, Problems Control & Inform. Theory, 12, No. 4, 1–13, 1983.

    MathSciNet  Google Scholar 

  17. M. Dyer, T. Fenner, A. Frieze, A. Thomason, “On key storage in secure networks”, J. of Cryptology, 8, 189–200, 1995.

    Article  MATH  Google Scholar 

  18. 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. of Math., 51, 75–89, 1985.

    Article  Google Scholar 

  19. M. Farach, S. Kannan, E. H. Knill and S. Muthukrishnan, “Group testing with sequences in experimental molecular biology”, Sequences 1997, IEEE Computer Society, 357–367.

    Google Scholar 

  20. F. Meyer auf der Heide, C. Scheideler, V. Stemann, “Exploiting storage redundancy to speed up randomized shared memory simulations”, STACS 95, 267–278.

    Google Scholar 

  21. F.K. Hwang, “A Tale of Two Coins”, Amer. Math. Monthly 94, 121–129, 1987.

    Article  MathSciNet  Google Scholar 

  22. F.K. Hwang and V. T. Sös, “Non adaptive hypergeometric group testing”, Studia Sc. Math. Hungarica, vol. 22, 257–263, 1987.

    MATH  Google Scholar 

  23. P. Indyk, “Deterministic superimposed coding with application to pattern matching”, FOCS 97, IEEE Press, 127–136.

    Google Scholar 

  24. G.O.H. Katona and T.G. Tarján, “Extremal problems with excluded subgraphs in the n-cube”, Lecture Notes in Math., 1018, Springer-Verlag, Berlin, 84–93, 1983.

    Google Scholar 

  25. I. Katzela and M. Naghshineh, “Channel assignment schemes for cellular mobile telecommunication systems: a comprehensive survey”, IEEE Personal Communications, 10–31, June 1996.

    Google Scholar 

  26. W. H. Kautz and R. R. Singleton, “Nonrandom binary superimposed codes”, IEEE Trans. on Inform. Theory, 10, 363–377, 1964.

    Article  MATH  Google Scholar 

  27. J. Komlós and A.G. Greenberg, “An asymptotically non-adaptive algorithm for conflict resolution in multiple-access channels”, IEEE Trans. on Inform. Theory, 31, No. 2, 302–306, 1985.

    Article  MATH  Google Scholar 

  28. N. Linial, “Locality in distributed graph algorithms”, SIAM J. on Computing, 21, 193–201, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  29. D. Margaritis and S. Skiena, “Reconstructing strings from substrings in rounds”, FOCS 95, 613–620.

    Google Scholar 

  30. P. A. Pevzner and R. Lipshutz, “Towards DNA sequencing chips”, MFCS 1994, Lectures Notes in Computer Science, 143–158, Springer Verlag.

    Google Scholar 

  31. M. Ruszinkó, “On the upper bound of the size of the r-cover-free families”, J. of Combinatorial Theory, Series A, 66, 302–310, 1994.

    Article  MATH  Google Scholar 

  32. Yu.L. Sagalovich, “Separating systems”, Problems of Information Transmission, 30, No. 2, 105–123, 1994.

    MATH  MathSciNet  Google Scholar 

  33. D.R. Stinson, Tran van Trung and R. Wei, “ Secure frameproof codes, key distribution patterns, group testing algorithms and related structures”, Journal of Statistical Planning and Inference, 86, 595–617, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  34. M. Szegedy and S. Vishwanathan, “Locality based graph coloring”, STOC 93, ACM Press, 201–207.

    Google Scholar 

  35. B. S. Tsybakov, V.A. Mikhailov and N.B. Likhanov, “Bounds for packet transmissions rate in a random-multiple-access system”, Problems of Information Transmission, 19, 61–81, 1983.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

De Bonis, A., Vaccaro, U. (2002). Efficient Constructions of Generalized Superimposed Codes with Applications to Group Testing and Conflict Resolution in Multiple Access Channels. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_32

Download citation

  • DOI: https://doi.org/10.1007/3-540-45749-6_32

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics