P. Berenbrink, Tom Friedetzky, Dominik Kaaser, Peter Kling
{"title":"Tight & Simple Load Balancing","authors":"P. Berenbrink, Tom Friedetzky, Dominik Kaaser, Peter Kling","doi":"10.1109/IPDPS.2019.00080","DOIUrl":null,"url":null,"abstract":"We consider the following load balancing process for m tokens distributed arbitrarily among n nodes connected by a complete graph. In each time step a pair of nodes is selected uniformly at random. Let ℓ_1 and ℓ_2 be their respective number of tokens. The two nodes exchange tokens such that they have ⌈(ℓ_1 + ℓ_2)/2⌉ and ⌈(ℓ_1 + ℓ_2)/2⌉ tokens, respectively. We provide a simple analysis showing that this process reaches almost perfect balance within O(n log n + n log Δ) steps with high probability, where Δ is the maximal initial load difference between any two nodes. This bound is asymptotically tight.","PeriodicalId":403406,"journal":{"name":"2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IPDPS.2019.00080","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
Abstract
We consider the following load balancing process for m tokens distributed arbitrarily among n nodes connected by a complete graph. In each time step a pair of nodes is selected uniformly at random. Let ℓ_1 and ℓ_2 be their respective number of tokens. The two nodes exchange tokens such that they have ⌈(ℓ_1 + ℓ_2)/2⌉ and ⌈(ℓ_1 + ℓ_2)/2⌉ tokens, respectively. We provide a simple analysis showing that this process reaches almost perfect balance within O(n log n + n log Δ) steps with high probability, where Δ is the maximal initial load difference between any two nodes. This bound is asymptotically tight.
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