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)
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
Revisiting randomized parallel load balancing algorithms
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
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We extend the lower bound of Adler et al. (1998) [1] and Berenbrink et al. (1999) [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 Adler et al. (1998) [1] and Berenbrink et al. (1999) [2], a lower bound of @W(logn/loglognr) is proved if the communication is limited to r rounds. Three assumptions appear in the proofs in Adler et al. (1998) [1] and Berenbrink et al. (1999) [2]: the topological assumption, random choices of confused balls, and symmetry. The topological assumption states that each ball's decision is based only on collisions between choices of balls. The confused ball assumption states that if a ball obtains the same topological information from all its chosen bins, then the ball commits to one of the chosen bins by flipping a fair coin. The symmetry assumption states that all the balls run identical algorithms, the same assumption holds for the bins. 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 (Adler et al., 1998 [1]; Berenbrink et al., 1999 [2]; Stemann, 1996 [3]; Even and Medina, 2009 [4]).