Abstract
We study the problem of contention resolution for different-sized jobs on a simple channel. When a job makes a run attempt, it learns only whether the attempt succeeded or failed. We first analyze binary exponential backoff, and show that it achieves a makespan of \(V2^{\Theta(\sqrt{\log{n}})}\) with high probability, where V is the total work of all n contending jobs. This bound is significantly larger than when jobs are constant sized. A variant of exponential backoff, however, achieves makespan O(V logV) with high probability. Finally, we introduce a new protocol, size-hashed backoff, specifically designed for jobs of multiple sizes that achieves makespan O(V log3logV). The error probability of the first two bounds is polynomially small in n and the latter is polynomially small in logV.
This research was supported in part by the Singapore-MIT Alliance, NSF Grants CCR-0208670, ITR-0121277, CNS-0305606, OCI-0324974, and by USAF/AFRL Award #FA9550-04-1-0121.
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Bender, M.A., Fineman, J.T., Gilbert, S. (2006). Contention Resolution with Heterogeneous Job Sizes. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_13
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DOI: https://doi.org/10.1007/11841036_13
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