TY - JOUR

T1 - Revisiting randomized parallel load balancing algorithms

AU - Even, Guy

AU - Medina, Moti

PY - 2012/7/27

Y1 - 2012/7/27

N2 - 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. (1998) [1] presented lower bounds and upper bounds for this problem. A similar lower bound appears in Berenbrink et al. (1999) [2]. The general 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 etal. (1998) [1]. We amend this situation by presenting proofs of the lower bound for these two specific 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 10 6≤n≤8·10 6 balls and bins. In fact, the obtained maximum load meets the best experimental results for sequential algorithms.

AB - 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. (1998) [1] presented lower bounds and upper bounds for this problem. A similar lower bound appears in Berenbrink et al. (1999) [2]. The general 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 etal. (1998) [1]. We amend this situation by presenting proofs of the lower bound for these two specific 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 10 6≤n≤8·10 6 balls and bins. In fact, the obtained maximum load meets the best experimental results for sequential algorithms.

KW - Balls and bins

KW - Static randomized parallel load balancing algorithms

UR - http://www.scopus.com/inward/record.url?scp=84861999054&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2012.01.009

DO - 10.1016/j.tcs.2012.01.009

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AN - SCOPUS:84861999054

SN - 0304-3975

VL - 444

SP - 87

EP - 99

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -