Revisiting randomized parallel load balancing algorithms

Guy Even, Moti Medina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We deal with the well studied allocation problem of assigning n balls to n bins so that the maximum number of balls assigned to the same bin is minimized. We focus on randomized, constant-round, distributed, asynchronous algorithms for this problem. Adler et al. [1] presented lower bounds and upper bounds for this problem. A similar lower bound appears in Berenbrink et al. [2]. The lower bound is based on a topological assumption. Our first contribution is the observation that the topological assumption does not hold for two algorithms presented by Adler et al. [1]. We amend this situation by presenting direct proofs of the lower bound for these two algorithms. We present an algorithm in which a ball that was not allocated in the first round retries with a new choice in the second round. We present tight bounds on the maximum load obtained by our algorithm. The analysis is based on analyzing the expectation and transforming it to a bound with high probability using martingale tail inequalities. Finally, we present a 3-round heuristic with a single synchronization point. We conducted experiments that demonstrate its advantage over parallel algorithms for 106 ≤ n ≤ 108 balls and bins. In fact, the obtained maximum load meets the best results for sequential algorithms.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 16th International Colloquium, SIROCCO 2009, Revised Selected Papers
Pages209-221
Number of pages13
DOIs
StatePublished - 2010
Event16th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009 - Piran, Slovenia
Duration: 25 May 200927 May 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5869 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009
Country/TerritorySlovenia
CityPiran
Period25/05/0927/05/09

Keywords

  • Balls and bins
  • Load balancing
  • Martingales
  • Static randomized parallel allocation

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