Unbounded Contention Resolution in Multiple-Access Channels

Antonio Fernandez Anta, Miguel A. Mosteiro and Jorge R. Muñoz

Abstract: 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 effcient 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, or the solution is suboptimal, or it is only implicit or embedded 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, tailoring the constants for our needs. In contrast with previous work, both protocols are proved to be optimal up to a small constant factor and with high probability for big enough number of contenders.

Guest: Antonio Fernandez Anta
Host: Yvonne-Anne Pignolet

Structuring Unreliable Radio Networks

Keren Censor-Hillel, Seth Gilbert, Fabian Kuhn, Nancy Lynch and Calvin Newport

Abstract: In this paper we study the problem of building a connected dominating set with constant degree (CCDS) in the dual graph radio network model [5, 10, 11]. This model includes two types of links: reliable, which always deliver messages, and unreliable, which sometimes fail to deliver messages. Real networks compensate for this differing quality by deploying low-layer detection protocols to filter unreliable from reliable links. With this in mind, we begin by presenting an algorithm that solves the CCDS problem in the dual graph model under the assumption that every process u is provided a local link detector set consisting of every neighbor connected to u by a reliable link. A natural follow up question is whether the link detector must be perfectly reliable to solve the CCDS problem. With this in mind, we first describe an algorithm that builds a CCDS in O(∆polylog(n)) time under the assumption of O(1) unreliable links included in each link detector set. We then prove this algorithm to be (almost) tight by showing that the possible inclusion of only a single unreliable link in each process’s local link detector set is sufficient to require Ω(∆) rounds to solve the CCDS problem, regardless of message size. We conclude by discussing how to apply our algorithm in the setting where the topology of reliable and unreliable links can change over time.

Guest: Calvin Newport
Host: Yvonne-Anne Pignolet