A guided tour of Chernoff bounds
Information Processing Letters
Randomized algorithms
SIAM Journal on Computing
Balanced allocations: the heavily loaded case
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Fast concurrent access to parallel disks
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Contention Resolution in Hashing Based Shared Memory Simulations
SIAM Journal on Computing
Reconciling simplicity and realism in parallel disk models
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Random Graphs, Random Walks, Differential Equations and the Probabilistic Analysis of Algorithms
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Fast Priority Queues for Cached Memory
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
Uniform hashing in constant time and linear space
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Almost random graphs with simple hash functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Journal of Algorithms
Efficient hashing with lookups in two memory accesses
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Asymmetric balanced allocation with simple hash functions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Linear probing with constant independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The k-orientability thresholds for Gn, p
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Linear Probing with 5-wise Independence
SIAM Review
Maintaining external memory efficient hash tables
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Practical perfect hashing in nearly optimal space
Information Systems
Simple and space-efficient minimal perfect hash functions
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We study an aspect of the balanced allocation paradigm (also known as the “two-choices paradigm”). Assume there are n balls and m =(1+ε) n /d bins of capacity d each, for a fixed d≥1. To each of the balls two possible bins are assigned at random. We show that ε (2/e)d−−1 is sufficient to guarantee that with high probability each ball can be put into one of the two bins assigned to it, without any bin overflowing. Further, it takes constant time on average for changing the arrangement to accommodate a new ball, if εγ·βd, for some constants γ0, βm positions, each representing a bucket of capacity d≥1. Key x may be stored in bucket h1(x) or h2(x), for two fully random hash functions h1 and h2. For arbitrary ε0, we obtain an implementation of a dynamic dictionary that accommodates n keys in m =(1+ε)n /d buckets of size d = O(log(1/ε)). For a lookup operation only two hash functions have to be evaluated and two contiguous segments of d memory cells have to be inspected. The expected time for inserting a new key is constant.