Private vs. common random bits in communication complexity

Newman, Ilan

doi:10.1016/0020-0190(91)90157-d

Cited by 283 publications

(180 citation statements)

References 3 publications

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“…One may wonder whether there exists a private-coin communication protocol with the same properties as the protocol of Theorem 3.1. Newman's theorem ( [6]) states that every public-coin protocol can be transformed into a private-coin protocol at the expense of increasing the error probability by δ and the worst case communication by O(log log |X × Y| + log 1/δ) (for any positive δ). Lemma 3.1 provides an upper bound for the error probability and communication of our protocol for each pair of inputs.…”

Section: Lemma 31 Let ε Be a Positive Real And H A Positive Integermentioning

confidence: 99%

On Slepian–Wolf Theorem with Interaction

Kozachinskiy

2017

Theory Comput Syst

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In this paper we study interactive "one-shot" analogues of the classical Slepian-Wolf theorem. Alice receives a value of a random variable X, Bob receives a value of another random variable Y that is jointly distributed with X. Alice's goal is to transmit X to Bob (with some error probability ε). Instead of one-way transmission, which is studied in the classical coding theory, we allow them to interact. They may also use shared randomness.We show, that Alice can transmit X to Bob in expected H(X|Y ) + 2 H(X|Y ) + O(log 2 1 ε ) number of bits. Moreover, we show that every one-round protocol π with information complexity I can be compressed to the (many-round) protocol with expected communication about I + 2 √ I bits. This improves a result by Braverman and Rao [3], where they had 5 √ I. Further, we show how to solve this problem (transmitting X) using 3H(X|Y ) + O(log 2 1 ε ) bits and 4 rounds on average. This improves a result of [4], where they had 4H(X|Y ) + O(log 1/ε) bits and 10 rounds on average.In the end of the paper we discuss how many bits Alice and Bob may need to communicate on average besides H(X|Y ). The main question is whether the upper bounds mentioned above are tight. We provide an example of (X, Y ), such that transmission of X from Alice to Bob with error probability ε requires H(X|Y ) + Ω log 2 1 ε bits on average.

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Section: Lemma 31 Let ε Be a Positive Real And H A Positive Integermentioning

confidence: 99%

On Slepian–Wolf Theorem with Interaction

Kozachinskiy

2017

Theory Comput Syst

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“…For a public-coin randomized cell-probing scheme, the sequence of random bits r ∈ {0, 1} * is shared between the cell-probing algorithm A and the table structure T , where the table T r B is now determined by both the database B and the random bits r. This makes no change to the family of data structures of polynomial size: by Newman's theorem [18], a public-coin cell-probing scheme can be transformed to a standard randomized cell-probing scheme, where the randomness is private to the cell-probing algorithm.…”

Section: Preliminariesmentioning

confidence: 99%

Randomized Approximate Nearest Neighbor Search with Limited Adaptivity

Liu

Pan

Yin

2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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We study the fundamental problem of approximate nearest neighbor search in d-dimensional Hamming space {0, 1}d . We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider algorithms in the cell-probe model with limited adaptivity, where the algorithm makes k rounds of parallel accesses to the data structure for a given k. For any k ≥ 1, we give a simple randomized algorithm solving the approximate nearest neighbor search using k rounds of parallel memory accesses, with O(k(log d) 1/k ) accesses in total. We also give a more sophisticated randomized algorithm using O(k + (O(1/k) ) memory accesses in k rounds for large enough k. Both algorithms use data structures of size polynomial in n, the number of points in the database.For the lower bound, we prove an Ω(lower bound for the total number of memory accesses required by any randomized algorithm solving the approximate nearest neighbor search within k ≤ log log d 2 log log log d rounds of parallel memory accesses on any data structures of polynomial size. This lower bound shows that our first algorithm is asymptotically optimal for any constant round k. And our second algorithm approaches the asymptotically optimal tradeoff between rounds and memory accesses, in a sense that the lower bound of memory accesses for any k 1 rounds can be matched by the algorithm within k 2 = O(k 1 ) rounds. In the extreme, for some large enough k = Θ log log d log log log d , our second algorithm matches the Θ log log d log log log d tight bound for fully adaptive algorithms for approximate nearest neighbor search due to Chakrabarti and Regev [10]. IntroductionNearest neighbor search is a fundamental theoretical problem in Computer Science, with enormously many applications in diverse fields. In the nearest neighbor search problem, we are given a database B of n points from a metric space X. The goal is to preprocess them into a data structure, such that given any query point x ∈ X, an algorithm with accessing to the data structure can find a database point in B that is closest to the query point x among all database points. An extensively studied case is when the metric space is the Hamming space X = {0, 1} d .It is conjectured that the nearest neighbor search is hard to solve by any data structures when the dimension d is high (e.g. d ≫ log n). This conjecture is sometimes referred as a case of the "curse of dimensionality" and is one of the central problems in the area of data structure lower

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“…The distinction between private and public random bits can be made, where in the public bit/coin model Alice and Bob see the same random bits and in the private they each have a different random source. Newman [45] has shown that up to an additive logarithmic term the models are the same. Rabin and Yao show for EQ that there exists a classical randomized protocol that only needs O(log(n)) bits: R 2 (EQ) = O(log(n)).…”

Section: Communication Complexitymentioning

confidence: 99%