On balls and bins with deletions

Richard Cole, Alan Frieze, Bruce M. Maggs, Michael Mitzenmacher, Andréa W. Richa, Ramesh Sitaraman, Eli Upfal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationRandomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings
PublisherSpringer Verlag
Pages145-158
Number of pages14
Volume1518
ISBN (Print)354065142X, 9783540651420
DOIs
StatePublished - 1998
Event2nd International Workshop on Randomization and Approximation Techniques in Computer Science, Random 1998 - Barcelona, Spain
Duration: Oct 8 1998Oct 10 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1518
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other2nd International Workshop on Randomization and Approximation Techniques in Computer Science, Random 1998
CountrySpain
CityBarcelona
Period10/8/9810/10/98

Fingerprint

Bins
Deletion
Ball
Load Balancing
Random variables
Resource allocation
Routing
Random variable
Cover
Scenarios
Line
Alternatives

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Cole, R., Frieze, A., Maggs, B. M., Mitzenmacher, M., Richa, A. W., Sitaraman, R., & Upfal, E. (1998). On balls and bins with deletions. In Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings (Vol. 1518, pp. 145-158). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1518). Springer Verlag. https://doi.org/10.1007/3-540-49543-6_12

On balls and bins with deletions. / Cole, Richard; Frieze, Alan; Maggs, Bruce M.; Mitzenmacher, Michael; Richa, Andréa W.; Sitaraman, Ramesh; Upfal, Eli.

Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings. Vol. 1518 Springer Verlag, 1998. p. 145-158 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1518).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cole, R, Frieze, A, Maggs, BM, Mitzenmacher, M, Richa, AW, Sitaraman, R & Upfal, E 1998, On balls and bins with deletions. in Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings. vol. 1518, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1518, Springer Verlag, pp. 145-158, 2nd International Workshop on Randomization and Approximation Techniques in Computer Science, Random 1998, Barcelona, Spain, 10/8/98. https://doi.org/10.1007/3-540-49543-6_12
Cole R, Frieze A, Maggs BM, Mitzenmacher M, Richa AW, Sitaraman R et al. On balls and bins with deletions. In Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings. Vol. 1518. Springer Verlag. 1998. p. 145-158. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-49543-6_12
Cole, Richard ; Frieze, Alan ; Maggs, Bruce M. ; Mitzenmacher, Michael ; Richa, Andréa W. ; Sitaraman, Ramesh ; Upfal, Eli. / On balls and bins with deletions. Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings. Vol. 1518 Springer Verlag, 1998. pp. 145-158 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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