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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Metcalfe, R.M., Boggs, D.R.: Ethernet: Distributed packet switching for local computer networks. CACM 19(7), 395–404 (1976)
Abramson, N.: The ALOHA system — another alternative for computer communications. In: Proc. of AFIPS FJCC, vol. 37, pp. 281–285 (1970)
Herlihy, M., Moss, J.E.B.: Transactional memory: Architectural support for lock-free data structures. In: Proc. of the 20th Intl. Conference on Computer Architecture, San Diego, California, pp. 289–300 (1993)
Rajwar, R., Goodman, J.R.: Speculative lock elision: Enabling highly concurrent multithreaded execution. In: Proc. of the 34th Annual Intl. Symposium on Microarchitecture, Austin, Texas, pp. 294–305 (2001)
Ananian, C.S., Asanović, K., Kuszmaul, B.C., Leiserson, C.E., Lie, S.: Unbounded transactional memory. In: Proc. of the 11th Intl. Symposium on High-Performance Computer Architecture, San Franscisco, California, pp. 316–327 (2005)
MacKenzie, P.D., Plaxton, C.G., Rajaraman, R.: On contention resolution protocols and associated probabilistic phenomena. JACM 45(2), 324–378 (1998)
Juels, A., Rivest, R.L., Szydlo, M.: The blocker tag: Selective blocking of RFID tags for consumer privacy. In: Conference on Computer and Communications Security, 103–111 (2003)
Finkenzeller, K.: RFID Handbook: Fundamentals and Applications in Contactless Smart Cards and Identification, 2nd edn. John Wiley & Sons, Chichester (2003), E-book at, books24x7.com
Geréb-Graus, M., Tsantilas, T.: Efficient optical communication in parallel computers. In: Proc. of the 4th Annual Symposium on Parallel Algorithms and Architectures, pp. 41–48 (1992)
Greenberg, R.I., Leiserson, C.E.: Randomized routing on fat-trees. Advances in Computing Research 5, 345–374 (1989)
Bender, M.A., Farach-Colton, M., He, S., Kuszmaul, B.C., Leiserson, C.E.: Adversarial contention resolution for simple channels. In: 17th Annual Symposium on Parallelism in Algorithms and Architectures, pp. 325–332 (2005)
Greenberg, A.G., Winograd, S.: A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels. JACM 32(3), 589–596 (1985)
Greenberg, A.G., Flajolet, P., Ladner, R.E.: Estimating the multiplicities of conflicts to speed their resolution in multiple access channels. JACM 34(2), 289–325 (1987)
Goldberg, L.A., Jerrum, M., Leighton, T., Rao, S.: Doubly logarithmic communication algorithms for optical-communication parallel computers. SIAM Journal on Computing 26(4), 1100–1119 (1997)
Goldberg, L.A., Matias, Y., Rao, S.: An optical simulation of shared memory. SIAM Journal on Computing 28(5), 1829–1847 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/11841036_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38875-3
Online ISBN: 978-3-540-38876-0
eBook Packages: Computer ScienceComputer Science (R0)