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Approximating the Size of a Radio Network in Beeping Model

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Structural Information and Communication Complexity (SIROCCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9988))

Abstract

In a single-hop radio network, nodes can communicate with each other by broadcasting to a shared wireless channel. In each time slot, all nodes receive feedback from the channel depending on the number of transmitters. In the Beeping Model, each node learns whether zero or at least one node have transmitted. In such a model, a procedure estimating the size of the network can be used for efficiently solving the problems of leader election or conflict resolution. We introduce a time-efficient uniform algorithm for size estimation of single-hop networks. With probability at least \(1-1/f\) our solution returns \((1+\varepsilon )\)-approximation of the network size n within \(\mathcal {O}\left( \log \log n+\log f/\varepsilon ^2\right) \) time slots. We prove that the algorithm is asymptotically time-optimal for any constant \(\varepsilon >0\).

This paper is supported by Polish National Science Center – decision number 2013/09/N/ST6/03440 (M. Kardas).

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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  MATH  Google Scholar 

  2. Bordim, J.L., Cui, J., Hayashi, T., Nakano, K., Olariu, S.: Energy-efficient initialization protocols for ad-hoc radio networks. In: Aggarwal, A., Pandu Rangan, C. (eds.) Algorithms and Computation. LNCS, vol. 1741, pp. 215–224. Springer, Heidelberg (1999). doi:10.1007/3-540-46632-0_23

    Chapter  Google Scholar 

  3. Caragiannis, I., Galdi, C., Kaklamanis, C.: Basic computations in wireless networks. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 533–542. Springer, Heidelberg (2005). http://dx.doi.org/10.1007/11602613_54

    Chapter  Google Scholar 

  4. Chakrabarti, A., Regev, O.: An optimal lower bound on the communication complexity of gap-hamming-distance. In: Fortnow, L., Vadhan, S.P. (eds.) Proceedings of the 43rd ACM Symposium on Theory of Computing, STOC 2011, San Jose, CA, USA, 6–8 June 2011, pp. 51–60. ACM (2011). http://doi.acm.org/10.1145/1993636.1993644

  5. Chassaing, P., Gerin, L.: Efficient estimation of the cardinality of large data sets. In: 4th Colloquium on Mathematics and Computer Science, DMTCS Proceedings, pp. 419–422 (2006)

    Google Scholar 

  6. Chen, B., Zhou, Z., Yu, H.: Understanding RFID counting protocols. In: Helal, S., Chandra, R., Kravets, R. (eds.) The 19th Annual International Conference on Mobile Computing and Networking, MobiCom 2013, Miami, FL, USA, 30 September–04 October 2013, pp. 291–302. ACM (2013). http://doi.acm.org/10.1145/2500423.2500431

  7. Cichoń, J., Lemiesz, J., Szpankowski, W., Zawada, M.: Two-phase cardinality estimation protocols for sensor networks with provable precision. In: Proceedings of WCNC 2012, Paris, France. IEEE (2012)

    Google Scholar 

  8. Cichoń, J., Lemiesz, J., Zawada, M.: On size estimation protocols for sensor networks. In: Proceedings of the 51th IEEE Conference on Decision and Control, CDC 10–13, Maui, HI, USA. pp. 5234–5239, Proceedings of 51st Annual Conference on Decision and Control (CDC). IEEE, December 2012

    Google Scholar 

  9. Cornejo, A., Kuhn, F.: Deploying wireless networks with beeps. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 148–162. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Flajolet, P., Fusy, E., Gandouet, O., Meunier, F.: Hyperloglog: the analysis of a near-optimal cardinality estimation algorithm. In: Proceedings of the Conference on Analysis of Algorithms (AofA 2007), pp. 127–146 (2007)

    Google Scholar 

  11. Flajolet, P., Martin, G.N.: Probabilistic counting algorithms for data base applications. J. Comput. Syst. Sci. 31(2), 182–209 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Giroire, F.: Order statistics and estimating cardinalities of massive data sets. Discrete Appl. Math. 157(2), 406–427 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Greenberg, A.G., Flajolet, P., Ladner, R.E.: Estimating the multiplicities of conflicts to speed their resolution in multiple access channels. J. ACM 34(2), 289–325 (1987). http://doi.acm.org/10.1145/23005.23006

    Article  MathSciNet  MATH  Google Scholar 

  14. Han, H., Sheng, B., Tan, C.C., Li, Q., Mao, W., Lu, S.: Counting RFID tags efficiently and anonymously. In: 29th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, INFOCOM 2010, 15–19 March 2010, San Diego, CA, USA, pp. 1028–1036. IEEE (2010). http://dx.doi.org/10.1109/INFCOM.2010.5461944

  15. Jurdziński, T., Kutyłowski, M., Zatopianski, J.: Energy-efficient size approximation of radio networks with no collision detection. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 279–289. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  16. Kabarowski, J., Kutyłowski, M., Rutkowski, W.: Adversary immune size approximation of single-hop radio networks. In: Cai, J.-Y., Cooper, S.B., Li, A. (eds.) TAMC 2006. LNCS, vol. 3959, pp. 148–158. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Kodialam, M.S., Nandagopal, T.: Fast and reliable estimation schemes in RFID systems. In: Gerla, M., Petrioli, C., Ramjee, R. (eds.) Proceedings of the 12th Annual International Conference on Mobile Computing and Networking, MOBICOM 2006, Los Angeles, CA, USA, 23–29 September 2006, pp. 322–333. ACM (2006). http://doi.acm.org/10.1145/1161089.1161126

  18. Kodialam, M.S., Nandagopal, T., Lau, W.C.: Anonymous tracking using RFID tags. In: 26th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, INFOCOM 2007, Anchorage, Alaska, USA, 6–12 May 2007, pp. 1217–1225. IEEE (2007). http://dx.doi.org/10.1109/INFCOM.2007.145

  19. Nakano, K., Olariu, S.: Energy-efficient initialization protocols for single-hop radio networks with no collision detection. IEEE Trans. Parallel Distrib. Syst. 11(8), 851–863 (2000)

    Article  Google Scholar 

  20. Nakano, K., Olariu, S.: Uniform leader election protocols for radio networks. IEEE Trans. Parallel Distrib. Syst. 13(5), 516–526 (2002). http://doi.ieeecomputersociety.org/10.1109/TPDS.2002.1003864

    Article  Google Scholar 

  21. Qian, C., Ngan, H., Liu, Y., Ni, L.M.: Cardinality estimation for large-scale RFID systems. IEEE Trans. Parallel Distrib. Syst. 22(9), 1441–1454 (2011). http://doi.ieeecomputersociety.org/10.1109/TPDS.2011.36

    Article  Google Scholar 

  22. Shahzad, M., Liu, A.X.: Every bit counts: fast and scalable RFID estimation. In: Akan, Ö.B., Ekici, E., Qiu, L., Snoeren, A.C. (eds.) The 18th Annual International Conference on Mobile Computing and Networking, Mobicom 2012, Istanbul, Turkey, 22–26 August 2012, pp. 365–376. ACM (2012). http://doi.acm.org/10.1145/2348543.2348588

  23. Whang, K.Y., Zanden, B.T.V., Taylor, H.M.: A linear-time probabilistic counting algorithm for database applications. ACM Trans. Database Syst. 15(2), 208–229 (1990)

    Article  Google Scholar 

  24. Willard, D.E.: Log-logarithmic selection resolution protocols in a multiple access channel. SIAM J. Comput. 15(2), 468–477 (1986). http://dx.doi.org/10.1137/0215032

    Article  MathSciNet  MATH  Google Scholar 

  25. Zheng, Y., Li, M.: ZOE: fast cardinality estimation for large-scale RFID systems. In: Proceedings of the IEEE INFOCOM 2013, Turin, Italy, 4–19 April 2013, pp. 908–916. IEEE (2013). http://dx.doi.org/10.1109/INFCOM.2013.6566879

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Authors and Affiliations

  1. ETH Zürich, Zürich, Switzerland

    Philipp Brandes & Roger Wattenhofer

  2. Department of Computer Science at the Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wrocław, Poland

    Marcin Kardas, Marek Klonowski & Dominik Pająk

Authors
  1. Philipp Brandes
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  2. Marcin Kardas
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  3. Marek Klonowski
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  4. Dominik Pająk
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  5. Roger Wattenhofer
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Corresponding author

Correspondence to Marcin Kardas .

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Editors and Affiliations

  1. Aalto University, Espoo, Finland

    Jukka Suomela

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Brandes, P., Kardas, M., Klonowski, M., Pająk, D., Wattenhofer, R. (2016). Approximating the Size of a Radio Network in Beeping Model. In: Suomela, J. (eds) Structural Information and Communication Complexity. SIROCCO 2016. Lecture Notes in Computer Science(), vol 9988. Springer, Cham. https://doi.org/10.1007/978-3-319-48314-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-48314-6_23

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