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)
Revisiting randomized parallel load balancing algorithms
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
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
Revisiting randomized parallel load balancing algorithms
Theoretical Computer Science
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We extend the lower bound of Adler et. al [1] and Berenbrink [2] for parallel randomized load balancing algorithms.The setting in these asynchronous and distributed algorithms is of n balls and n bins. The algorithms begin by each ball choosing d bins independently and uniformly at random. The balls and bins communicate to determine the assignment of each ball to a bin. The goal is to minimize the maximum load, i.e., the number of balls that are assigned to the same bin. In [1,2], a lower bound of $\Omega(\sqrt[r]{ \log n / \log \log n})$ is proved if the communication is limited to r rounds.Three assumptions appear in the proofs in [1,2]: the topological assumption, random choices of confused balls, and symmetry. We extend the proof of the lower bound so that it holds without these three assumptions. This lower bound applies to every parallel randomized load balancing algorithm we are aware of [1,2,3,4].