Paper Info
Title
Smoothed analysis of balancing networks
Abstract
In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to some predefined rule. As it turns out, this rule crucially affects the performance of the network. In this work we propose a model that studies this effect. We suggest a model bridging the uniformly-random assignment rule, and the arbitrary one (in the spirit of smoothed-analysis). We start with an arbitrary assignment of balancer directions and then flip each assignment with probability α independently. For a large class of balancing networks our result implies that after \documentclass{article} \usepackage{amsmath,amsfonts,mathrsfs}\pagestyle{empty}\begin{document} $\mathcal{O}(\log n)$ \end{document} rounds the discrepancy is \documentclass{article} \usepackage{amsmath,amsfonts,mathrsfs}\pagestyle{empty}\begin{document} $\mathcal{O}( (1/2-\alpha) \log n + \log \log n)$ \end{document} with high probability. This matches and generalizes known upper bounds for α = 0 and α = 1/2. We also show that a natural network matches the upper bound for any α. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 115–138, 2011 (A conference version of this article appeared in the 36th International Colloquium on Automata, Languages and Programming (ICALP 2009).)
Year
DOI
Venue
2011
10.1002/rsa.20341
international colloquium on automata, languages and programming
Keywords
DocType
Volume
smoothed analysis,arbitrary assignment,rule crucially,high probability,predefined rule,natural network,uniformly-random assignment rule,balancing network,inc. random struct,log n,upper bound,load balance,random assignment,col
Journal
39
Issue
ISSN
Citations 
1
1042-9832
5
PageRank 
References 
Authors
0.46
21
3
Name
Order
Citations
PageRank
Tobias Friedrich145723.56
Thomas Sauerwald257539.99
Dan Vilenchik314313.36