Parallel randomized load balancing: A lower bound for a more general model

Guy Even, Moti Medina

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

8 Scopus citations

Abstract

We extend the lower bound of Adler et. al [1] and Berenbrink [2] for parallel randomized load balancing algorithms. The setting in these asynchronous and distributed algorithms is of n balls and n bins. The algorithms begin by each ball choosing d bins independently and uniformly at random. The balls and bins communicate to determine the assignment of each ball to a bin. The goal is to minimize the maximum load, i.e., the number of balls that are assigned to the same bin. In [1,2], a lower bound of Ω (r√log n/ log log n)is proved if the communication is limited to r rounds. Three assumptions appear in the proofs in [1,2]: the topological assumption, random choices of confused balls, and symmetry. We extend the proof of the lower bound so that it holds without these three assumptions. This lower bound applies to every parallel randomized load balancing algorithm we are aware of [1,2,3,4].

Original languageEnglish
Title of host publicationSOFSEM 2010
Subtitle of host publicationTheory and Practice of Computer Science - 36th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
Pages358-369
Number of pages12
DOIs
StatePublished - 1 Mar 2010
Externally publishedYes
Event36th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2010 - Spindleruv Mlyn, Czech Republic
Duration: 23 Jan 201029 Jan 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5901 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference36th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2010
Country/TerritoryCzech Republic
CitySpindleruv Mlyn
Period23/01/1029/01/10

Keywords

  • Balls and bins
  • Load balancing
  • Lower bounds
  • Static randomized parallel allocation

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