Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Parallel randomized load balancing
Random Structures & Algorithms
SIAM Journal on Computing
Contention Resolution in Hashing Based Shared Memory Simulations
SIAM Journal on Computing
"Balls into Bins" - A Simple and Tight Analysis
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
How asymmetry helps load balancing
Journal of the ACM (JACM)
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Parallel Randomized Load Balancing: A Lower Bound for a More General Model
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Parallel randomized load balancing: A lower bound for a more general model
Theoretical Computer Science
Tight bounds for parallel randomized load balancing: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
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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.