Unbounded Contention Resolution in Multiple-Access Channels
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A frequent problem in settings where a unique resource must be shared among users is how to resolve the contention that arises when all of them must use it, but the resource allows only for one user each time. The application of efficient solutions for this problem spans a myriad of settings such as radio communication networks or databases. For the case where the number of users is unknown, recent work has yielded fruitful results for local area networks and radio networks, although either a (possibly loose) upper bound on the number of users needs to be known (Fernández Anta and Mosteiro in Discrete Math., Algorithms Appl. 2(4):445–456, 2010), or the solution is suboptimal (Bender et al. in ACM 17th Annual Symposium on Parallel Al- gorithms and Architectures, pp. 325–332, 2005), or it is only implicit (Greenberg and Leiserson in Adv. Comput. Res. 5:345–374, 1989) or embedded (Farach-Colton et al. in Theor. Comput. Sci. 472:60–80, 2013) in other problems, with bounds proved only asymptotically. In this paper, under the assumption that collision detection or information on the number of contenders is not available, we present a novel protocol for contention resolution in radio networks, and we recreate a protocol previously used for other problems (Greenberg and Leiserson in Adv. Comput. Res. 5:345–374, 1989, Farach-Colton et al. in Theor. Comput. Sci. 472:60–80, 2013), tailoring the constants for our needs. In contrast with previous work, both protocols are proved to be opti- mal up to a small constant factor and with high probability for big enough number of contenders. Additionally, the protocols are evaluated and contrasted with the previ- ous work by extensive simulations. The evaluation shows that the complexity bounds obtained by the analysis are rather tight, and that both protocols proposed have small and predictable complexity for many system sizes (unlike previous protocols).