Fast Pseudorandomness for Independence and Load Balancing

Meka, Raghu; Reingold, Omer; Rothblum, Guy N.; Rothblum, Ron D.

doi:10.1007/978-3-662-43948-7_71

Cited by 11 publications

(10 citation statements)

References 43 publications

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“…Then we show this hash family guarantees a load balancing of log log n d log φ d + O(1) in the Always-Go-Left scheme [Vöc03] with d choices. Notice that the constant φ d in equation At the same time, Our hash family has an evaluation time O (log log n) 4 in the RAM model based on the algorithm designed by Meka et al [MRRR14] for the hash family of Celis et al [CRSW13]. Finally, we show our hash family guarantees the same maximum load as a perfectly random hash function in the 1-choice scheme for m = n • poly(log n) balls.…”

Section: Our Contributionmentioning

confidence: 72%

“…At the same time, Our hash family has an evaluation time O (log log n) 4 in the RAM model based on the algorithm designed by Meka et al [MRRR14] for the hash family of Celis et al [CRSW13]. Finally, we show our hash family guarantees the same maximum load as a perfectly random hash function in the 1-choice scheme for m = n · poly(log n) balls.…”

Section: Our Contributionmentioning

confidence: 75%

“…For the hash family designed by Celis et al [CRSW13], Meka et al [MRRR14] improved the evaluation time of [CRSW13] to O((log log n) 2 ).…”

Section: Previous Workmentioning

confidence: 99%

“…. , h k use 1/poly(n)-biased spaces, which have total evaluation time O(k • log log n) = O(log log n) 2 in the RAM model from [MRRR14].…”

Section: Hash Functionsmentioning

confidence: 99%

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Derandomized Balanced Allocation

Chen¹

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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In this paper, we study the maximum loads of explicit hash families in the d-choice schemes when allocating sequentially n balls into n bins. We consider the Uniform-Greedy scheme [ABKU99], which provides d independent bins for each ball and places the ball into the bin with the least load, and its non-uniform variant -the Always-Go-Left scheme introduced by Vöcking [Vöc03]. We construct a hash family with O(log n log log n) random bits based on the previous work of Celis et al.[CRSW13] and show the following results.1. With high probability, this hash family has a maximum load of log log n log d + O(1) in the Uniform-Greedy scheme.2. With high probability, it has a maximum load of log log n d log φ d + O(1) in the Always-Go-Left scheme for a constant φ d > 1.61.The maximum loads of our hash family match the maximum loads of a perfectly random hash function [ABKU99, Vöc03] in the Uniform-Greedy and Always-Go-Left scheme separately, up to the low order term of constants. Previously, the best known hash families matching the same maximum loads of a perfectly random hash function in d-choice schemes were O(log n)-wise independent functions [Vöc03], which needs Θ(log 2 n) random bits.

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Section: Our Contributionmentioning

confidence: 72%

Section: Our Contributionmentioning

confidence: 75%

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Derandomized Balanced Allocation

Chen¹

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Naor and Naor [18] showed that relaxing from k-wise to almost k-wise independence can imply significant savings in the family size. As we we also care about the evaluation time of the functions, we will employ a very recent result of Meka, Reingold, Rothblum and Rothblum [16] (which, using Lemma 2.11, also applies to adaptive almost k-wise independence). The following is specialized from their work to the parameters we mostly care about in this work.…”

Section: Definition 28 (Statistical Distance) For Random Variables X ...mentioning

confidence: 99%

New techniques and tighter bounds for local computation algorithms

Reingold

Vardi

2016

Journal of Computer and System Sciences

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Given an input x, and a search problem F , local computation algorithms (LCAs) implement access to specified locations of y in a legal output y ∈ F (x), using polylogarithmic time and space. Mansour et al., (2012), had previously shown how to convert certain online algorithms to LCAs. In this work, we expand on that line of work and develop new techniques for designing LCAs and bounding their space and time complexity. Our contributions are fourfold: (1) We significantly improve the running times and space requirements of LCAs for previous results, (2) we expand and better define the family of online algorithms which can be converted to LCAs using our techniques, (3) we show that our results apply to a larger family of graphs than that of previous results, and (4) our proofs are simpler and more concise than the previous proof methods.For example, we show how to construct LCAs that require O(log n log log n) space and O(log 2 n) time (and expected time O(log log n)) for problems such as maximal matching on a large family of graphs, as opposed to the henceforth best results that required O(log 3 n) space and O(log 4 n) time, and applied to a smaller family of graphs.

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