TY - GEN

T1 - Revisiting randomized parallel load balancing algorithms

AU - Even, Guy

AU - Medina, Moti

PY - 2010/3/22

Y1 - 2010/3/22

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. [1] presented lower bounds and upper bounds for this problem. A similar lower bound appears in Berenbrink et al. [2]. The 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 et al. [1]. We amend this situation by presenting direct proofs of the lower bound for these two 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 106 ≤ n ≤ 108 balls and bins. In fact, the obtained maximum load meets the best 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. [1] presented lower bounds and upper bounds for this problem. A similar lower bound appears in Berenbrink et al. [2]. The 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 et al. [1]. We amend this situation by presenting direct proofs of the lower bound for these two 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 106 ≤ n ≤ 108 balls and bins. In fact, the obtained maximum load meets the best results for sequential algorithms.

KW - Balls and bins

KW - Load balancing

KW - Martingales

KW - Static randomized parallel allocation

UR - http://www.scopus.com/inward/record.url?scp=77949448228&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11476-2_17

DO - 10.1007/978-3-642-11476-2_17

M3 - Conference contribution

AN - SCOPUS:77949448228

SN - 364211475X

SN - 9783642114755

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

SP - 209

EP - 221

BT - Structural Information and Communication Complexity - 16th International Colloquium, SIROCCO 2009, Revised Selected Papers

T2 - 16th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009

Y2 - 25 May 2009 through 27 May 2009

ER -