Generalized Selectors and Locally Thin Families with Applications to Conflict Resolution in Multiple Access Channels Supporting Simultaneous Successful Transmissions

Author Annalisa De Bonis

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Annalisa De Bonis

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Annalisa De Bonis. Generalized Selectors and Locally Thin Families with Applications to Conflict Resolution in Multiple Access Channels Supporting Simultaneous Successful Transmissions. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We consider the Conflict Resolution Problem in the context of a multiple-access system in which several stations can transmit their messages simultaneously to the channel. We assume that there are n stations and that at most k, k <= n, stations are active at the same time, i.e, are willing to transmit a message over the channel. If in a certain instant at most d, d <= k, active stations transmit to the channel then their messages are successfully transmitted, whereas if more than d active stations transmit simultaneously then their messages are lost. In this latter case we say that a conflict occurs. The present paper investigates non-adaptive conflict resolution algorithms working under the assumption that active stations receive a feedback from the channel that informs them on whether their messages have been successfully transmitted. If a station becomes aware that its message has been correctly sent over the channel then it becomes immediately inactive, that is, stops transmitting. The measure to optimize is the number of time slots needed to solve conflicts among all active stations. The fundamental question is how much this measure decreases with the number d of messages that can be simultaneously transmitted with success. In this paper we prove that it is possible to achieve a speedup linear in d by providing a conflict resolution algorithm that uses a 1/d ratio of the number of time slots used by the optimal conflict resolution algorithm for the particular case d = 1. Moreover, we derive a lower bound on the number of time slots needed to solve conflicts non-adaptively which is within a log(k/d) factor from the upper bound. To the aim of proving these results, we introduce a new combinatorial structure that consists in a generalization of Komlós and Greenberg codes. Constructions of these new codes are obtained via a new kind of selectors, whereas the non-existential result is implied by a non-existential result for a new generalization of the locally thin families. We believe that the combinatorial structures introduced in this paper and the related results may be of independent interest.
  • Multiple-Access channels
  • Multi Access Communication
  • Conflict Resolutions
  • New Combinatorial Structures
  • Selectors


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  1. Noga Alon, Emanuela Fachini, and János Körner. Locally thin set families. Combinatorics, Probability and Computing, 9(06):481-488, 2000. Google Scholar
  2. Noga Alon and Joel Spencer. The Probabilistic Method. Interscience series in discrete mathematics and optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley &Sons, Inc., Hoboken, NJ,, third edition, 2008. Google Scholar
  3. Stefano Basagni, Danilo Bruschi, and Imrich Chlamtac. A mobility-transparent deterministic broadcast mechanism for ad hoc networks. IEEE/ACM transactions on networking, 7(6):799-807, 1999. Google Scholar
  4. Keren Censor-Hillel, Bernhard Haeupler, Nancy Lynch, and Muriel Médard. Bounded-contention coding for the additive network model. Distributed Computing, 28(5):297-308, 2015. Google Scholar
  5. Douglas S. Chan, Toby Berger, and Lang Tong. Carrier sense multiple access communications on multipacket reception channels: theory and applications to IEEE 802.11 wireless networks. IEEE Transactions on Communications, 61(1):266-278, 2013. Google Scholar
  6. Bogdan S. Chlebus. Randomized communication in radio networks. In P. M. Pardalos, S. Rajasekaran, J. Reif, and J. D. P. Rolim, editors, Handbook of Randomized Computing, volume 1, pages 401-456. Kluwer Academic Publishers, 2001. Google Scholar
  7. Bogdan S. Chlebus, Leszek Gąsieniec, Alan Gibbons, Andrzej Pelc, and Wojciech Rytter. Deterministic broadcasting in unknown radio networks. In Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'00, pages 861-870, Philadelphia, PA, USA, 2000. Society for Industrial and Applied Mathematics. Google Scholar
  8. Andrea E. F. Clementi, Angelo Monti, and Riccardo Silvestri. Selective families, superimposed codes, and broadcasting on unknown radio networks. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 709-718. Society for Industrial and Applied Mathematics, 2001. Google Scholar
  9. Gérard D. Cohen. Applications of coding theory to communication combinatorial problems. Discrete Mathematics, 83(2):237-248, 1990. Google Scholar
  10. Miklós Csűrös and Miklós Ruszinkó. Single-user tracing and disjointly superimposed codes. IEEE transactions on information theory, 51(4):1606-1611, 2005. Google Scholar
  11. Annalisa De Bonis, Leszek Gąsieniec, and Ugo Vaccaro. Optimal two-stage algorithms for group testing problems. SIAM Journal on Computing, 34(5):1253-1270, 2005. Google Scholar
  12. Annalisa De Bonis and Ugo Vaccaro. Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels. Theoretical Computer Science, 306(1):223-243, 2003. Google Scholar
  13. Annalisa De Bonis and Ugo Vaccaro. Optimal algorithms for two group testing problems, and new bounds on generalized superimposed codes. IEEE transactions on information theory, 52(10):4673-4680, 2006. Google Scholar
  14. Aditya Dua. Random access with multi-packet reception. IEEE Transactions on Wireless Communications, 7(6):2280-2288, 2008. Google Scholar
  15. Jörg Flum and Martin Grohe. Parameterized Complexity Theory. Springer, 2006. Google Scholar
  16. Sylvie Ghez, Sergio Verdu, and Stuart C. Schwartz. Stability properties of slotted aloha with multipacket reception capability. IEEE Transactions on Automatic Control, 33(7):640-649, 1988. Google Scholar
  17. Sylvie Ghez, Sergio Verdú, and Stuart C. Schwartz. Optimal decentralized control in the random access multipacket channel. IEEE Transactions on Automatic Control, 34(11):1153-1163, 1989. Google Scholar
  18. Jasper Goseling, Michael Gastpar, and Jos H. Weber. Random access with physical-layer network coding. IEEE Transactions on Information Theory, 61(7):3670-3681, 2015. Google Scholar
  19. Albert G. Greenberg and Schmuel Winograd. A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels. Journal of the ACM (JACM), 32(3):589-596, 1985. Google Scholar
  20. Janos Komlos and Albert Greenberg. An asymptotically fast nonadaptive algorithm for conflict resolution in multiple-access channels. IEEE Transactions on Information Theory, 31(2):302-306, 1985. Google Scholar
  21. Dariusz R. Kowalski. On selection problem in radio networks. In Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing, pages 158-166. ACM, 2005. Google Scholar
  22. Avery Miller. On the complexity of neighbourhood learning in radio networks. Theoretical Computer Science, 608:135-145, 2015. Google Scholar
  23. Robin A. Moser and Gábor Tardos. A constructive proof of the general lovász local lemma. Journal of the ACM (J. ACM), 57(2):11-15, 2010. Google Scholar
  24. Alexander Russell, Sudarshan Vasudevan, Bing Wang, Wei Zeng, Xian Chen, and Wei Wei. Neighbor discovery in wireless networks with multipacket reception. IEEE Transactions on Parallel and Distributed Systems, 26(7):1984-1998, 2015. Google Scholar
  25. Boris Tsybakov. Packet multiple access for channel with binary feedback, capture, and multiple reception. IEEE Transactions on Information Theory, 50(6):1073-1085, 2004. Google Scholar