An information statistics approach to data stream and communication complexity
Ziv Bar-Yossef,T. S. Jayram,Ravi Kumar,Dandapani Sivakumar +3 more
- Vol. 68, Iss: 4, pp 209-218
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This work presents a new method for proving strong lower bounds in communication complexity based on the notion of the conditional information complexity of a function, and shows that it also admits a direct sum theorem.Abstract:
We present a new method for proving strong lower bounds in communication complexity. This method is based on the notion of the conditional information complexity of a function which is the minimum amount of information about the inputs that has to be revealed by a communication protocol for the function. While conditional information complexity is a lower bound on the communication complexity, we show that it also admits a direct sum theorem. Direct sum decomposition reduces our task to that of proving (conditional) information complexity lower bounds for simple problems (such as the AND of two bits). For the latter, we develop novel techniques based on Hellinger distance and its generalizations.read more
Citations
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Journal ArticleDOI
Data streams: algorithms and applications
TL;DR: Data Streams: Algorithms and Applications surveys the emerging area of algorithms for processing data streams and associated applications, which rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity.
Book
Data Streams: Algorithms and Applications
TL;DR: In this paper, the authors present a survey of basic mathematical foundations for data streaming systems, including basic mathematical ideas, basic algorithms, and basic algorithms and algorithms for data stream processing.
Journal ArticleDOI
Index Coding With Side Information
TL;DR: A measure on graphs, the minrank, is identified, which exactly characterizes the minimum length of linear and certain types of nonlinear INDEX codes and for natural classes of side information graphs, including directed acyclic graphs, perfect graphs, odd holes, and odd anti-holes, minrank is the optimal length of arbitrary INDex codes.
Journal ArticleDOI
Asymptotics in Statistics–Some Basic Concepts
TL;DR: In this article, the convergence of Distri butions of Likelihood Ratio has been discussed, and the authors propose a method to construct a set of limit laws for Likelihood Ratios.
Proceedings ArticleDOI
Index Coding with Side Information
TL;DR: A measure on graphs, the minrank, is identified, which exactly characterizes the minimum length of linear and certain types of nonlinear INDEX codes and for natural classes of side information graphs, including directed acyclic graphs, perfect graphs, odd holes, and odd anti-holes, minrank is the optimal length of arbitrary INDex codes.
References
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Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
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Communication Complexity
Eyal Kushilevitz,Noam Nisan +1 more
TL;DR: This chapter surveys the theory of two-party communication complexity and presents results regarding the following models of computation: • Finite automata • Turing machines • Decision trees • Ordered binary decision diagrams • VLSI chips • Networks of threshold gates.