Efficient PRAM simulation on a distributed memory machine
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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
The power of two choices in randomized load balancing
The power of two choices in randomized load balancing
Balanced Allocations: The Heavily Loaded Case
SIAM Journal on Computing
Balanced allocations with heterogenous bins
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Balanced allocations: the weighted case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Tight bounds for parallel randomized load balancing: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
A generalization of multiple choice balls-into-bins
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well-known that the gap between the load of the most loaded bin and the average is Θ (√mlog n/n), for large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to Θ (log log n) independent of m. Consider now the following "(1 + β)-choice" process for some parameter β ∈ (0, 1): each ball goes to a random bin with probability (1 - β) and the lesser loaded of two random bins with probability β. How does the gap for such a process behave? Suppose that the weight of each ball was drawn from a geometric distribution. How is the gap (now defined in terms of weight) affected? In this work, we develop general techniques for analyzing such balls-into-bins processes. Specifically, we show that for the (1 + β)-choice process above, the gap is Θ(log n/β), irrespective of m. Moreover the gap stays at Θ(log n/β) in the weighted case for a large class of weight distributions. No non-trivial explicit bounds were previously known in the weighted case, even for the 2-choice paradigm.