Abstract
We consider the problem of extending the analysis of balls and bins processes where a ball is placed in the least loaded of d randomly chosen bins to cover deletions. In particular, we are interested in the case where the system maintains a fixed load, and deletions are determined by an adversary before the process begins. We show that with high probability the load in any bin is O(log log n). In fact, this result follows from recent work by Cole et al. concerning a more difficult problem of routing in a butterfly network.
The main contribution of this paper is to give a different proof of this bound, which follows the lines of the analysis of Azar, Broder, Karlin, and Upfal for the corresponding static load balancing problem. We also give a specialized (and hence simpler) version of the argument from the paper by Cole et al. for the balls and bins scenario. Finally, we provide an alternative analysis also based on the approach of Azar, Broder, Karlin, and Upfal for the special case where items are deleted according to their age. Although this analysis does not yield better bounds than our argument for the general case, it is interesting because it utilizes a two-dimensional family of random variables in order to account for the age of the items. This technique may be of more general use.
Supported by NSF grants CCR-9503309 and CCR-9800085.
Supported by NSF grant CCR-9530974.
Supported in part by the Air Force Materiel Command. (AFMC) and ARPA under Contract F196828-93-C-0193, by ARPA Contracts F33615-93-1-1330 and N00014-95-1-1246, and by an NSF National Young Investigator Award, No. CCR-94-57766, with matching funds provided by NEC Research Institute and Sun Microsystems. The views and conclusions contained here are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either express or implied, of AFMC, ARPA, CMU, or the U.S. Government.
Supported in part by an NSF National Young Investigator Award, No. CCR-94-57766, with matching funds provided by NEC Research Institute and Sun Microsystems.
Supported in part by an NSF CAREER Award No. CCR-97-03017.
Supported in part by NSF grant CCR-9731477.
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Cole, R. et al. (1998). On Balls and Bins with Deletions. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_12
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