TY - GEN

T1 - Smoothed analysis of balancing networks

AU - Friedrich, Tobias

AU - Sauerwald, Thomas

AU - Vilenchik, Dan

N1 - Funding Information:
Tobias Friedrich and Thomas Sauerwald were partially supported by postdoctoral fellowships from the German Academic Exchange Service (DAAD).

PY - 2009/11/12

Y1 - 2009/11/12

N2 - In a load 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 effects 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) by starting from an arbitrary assignment of balancer directions, then flipping each assignment with probability α independently. For a large class of balancing networks our result implies that after O (log n)rounds the discrepancy is whp . O((1/2-α)log n + log log n)This matches and generalizes the known bounds for α= 0 and α= 1/2.

AB - In a load 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 effects 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) by starting from an arbitrary assignment of balancer directions, then flipping each assignment with probability α independently. For a large class of balancing networks our result implies that after O (log n)rounds the discrepancy is whp . O((1/2-α)log n + log log n)This matches and generalizes the known bounds for α= 0 and α= 1/2.

UR - http://www.scopus.com/inward/record.url?scp=70449092007&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02930-1_39

DO - 10.1007/978-3-642-02930-1_39

M3 - Conference contribution

AN - SCOPUS:70449092007

SN - 3642029299

SN - 9783642029295

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 472

EP - 483

BT - Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings

T2 - 36th International Colloquium on Automata, Languages and Programming, ICALP 2009

Y2 - 5 July 2009 through 12 July 2009

ER -