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Optimal Multi-broadcast with Beeps Using Group Testing

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Structural Information and Communication Complexity (SIROCCO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11639))

Abstract

The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we obtain time-optimal and deterministic solutions for the fundamental communication task of multi-broadcast. The proposed solutions are completely uniform, i.e., independent of the network and problem parameters.

We improve on previous results for multi-broadcast by giving efficiently constructible solutions, that is, with local computation cost polynomial in the identifiers’ range. The originality of our approach lies in the use of (combinatorial) group testing strategies, originally developed in the centralized context.

Supported by the Centre for Discrete Mathematics and its Applications (DIMAP) and by EPSRC award EP/N011163/1. The full version of this paper can be found at https://hal.archives-ouvertes.fr/hal-02140017.

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References

  1. Afek, Y., Alon, N., Bar-Joseph, Z., Cornejo, A., Haeupler, B., Kuhn, F.: Beeping a maximal independent set. Distrib. Comput. 26(4), 195–208 (2013)

    Article  Google Scholar 

  2. Bar-Yehuda, R., Israeli, A., Itai, A.: Multiple communication in multihop radio networks. SIAM J. Comput. 22(4), 875–887 (1993)

    Article  MathSciNet  Google Scholar 

  3. Bonis, A., Gasieniec, L., Vaccaro, U.: Optimal two-stage algorithms for group testing problems. SIAM J. Comput. 34(5), 1253–1270 (2005)

    Article  MathSciNet  Google Scholar 

  4. Cheraghchi, M.: Noise-resilient group testing: limitations and constructions. Discrete Appl. Math. 161(1), 81–95 (2013)

    Article  MathSciNet  Google Scholar 

  5. Chlebus, B.S., Kowalski, D.R., Pelc, A., Rokicki, M.A.: Efficient distributed communication in ad-hoc radio networks. In: ICALP, pp. 613–624 (2011)

    Google Scholar 

  6. Cicalese, F., Vaccaro, U.: Superselectors: efficient constructions and applications. In: ESA, pp. 207–218 (2010)

    Google Scholar 

  7. Cornejo, A., Kuhn, F.: Deploying wireless networks with beeps. In: DISC, pp. 148–162 (2010)

    Google Scholar 

  8. Czumaj, A., Davies, P.: Communicating with beeps. In: OPODIS, pp. 1–16 (2016)

    Google Scholar 

  9. Czumaj, A., Davies, P.: Deterministic communication in radio networks. SIAM J. Comput. 47(1), 218–240 (2018)

    Article  MathSciNet  Google Scholar 

  10. Czumaj, A., Davies, P.: Communicating with beeps. J. Parallel Distrib. Comput. (2019)

    Google Scholar 

  11. Dorfman, R.: The detection of defective members of large populations. Ann. Math. Statist. 14(4), 436–440 (1943)

    Article  Google Scholar 

  12. Du, D.Z., Hwang, F.K.: Combinatorial Group Testing and Its Applications. World Scientific, Singapore (1993)

    Book  Google Scholar 

  13. Dufoulon, F., Burman, J., Beauquier, J.: Beeping a deterministic time-optimal leader election. In: DISC, pp. 20:1–20:17 (2018)

    Google Scholar 

  14. D’yachkov, A., Rykov, V., Rashad, A.: Superimposed distance codes. Prob. Control Inf. Theory 18(4), 237–250 (1989)

    MathSciNet  MATH  Google Scholar 

  15. Ghaffari, M., Haeupler, B.: Near optimal leader election in multi-hop radio networks. In: SODA, pp. 748–766 (2013)

    Google Scholar 

  16. Hwang, F.K.: A method for detecting all defective members in a population by group testing. J. Am. Stat. Assoc. 67(339), 605–608 (1972)

    Article  Google Scholar 

  17. Indyk, P., Ngo, H.Q., Rudra, A.: Efficiently decodable non-adaptive group testing. In: SODA, pp. 1126–1142 (2010)

    Google Scholar 

  18. Li, C.H.: A sequential method for screening experimental variables. J. Am. Stat. Assoc. 57(298), 455–477 (1962)

    Article  MathSciNet  Google Scholar 

  19. Luo, J., Guo, D.: Neighbor discovery in wireless ad hoc networks based on group testing. In: 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 791–797 (2008)

    Google Scholar 

  20. Ngo, H.Q., Porat, E., Rudra, A.: Efficiently decodable error-correcting list disjunct matrices and applications. In: ICALP, pp. 557–568 (2011)

    Chapter  Google Scholar 

  21. Porat, E., Rothschild, A.: Explicit nonadaptive combinatorial group testing schemes. IEEE Trans. Inf. Theory 57(12), 7982–7989 (2011)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. LRI, CNRS UMR 8623, Université Paris-Sud, Université Paris-Saclay, Orsay, France

    Joffroy Beauquier, Janna Burman & Fabien Dufoulon

  2. University of Warwick, Coventry, UK

    Peter Davies

Authors
  1. Joffroy Beauquier
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  2. Janna Burman
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  3. Peter Davies
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  4. Fabien Dufoulon
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Corresponding author

Correspondence to Fabien Dufoulon .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Keren Censor-Hillel

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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Beauquier, J., Burman, J., Davies, P., Dufoulon, F. (2019). Optimal Multi-broadcast with Beeps Using Group Testing. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_5

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  • DOI: https://doi.org/10.1007/978-3-030-24922-9_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24921-2

  • Online ISBN: 978-3-030-24922-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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