Lower Bound Methods for Multiparty Communication Complexity PDF Download
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Author: Jeffrey Stephen Ford
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages :
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Author: Jeffrey Stephen Ford
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages :
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Author: Troy Lee
Publisher: Now Publishers Inc
ISBN: 1601982585
Category : Computers
Languages : en
Pages : 152
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Book Description
The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph surveys lower bounds in the field of communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to find a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communication complexity measure. Lower bounds on this geometric complexity measure are then found using algebraic and geometric tools.
Author: Tim Roughgarden
Publisher: Foundations and Trends (R) in Theoretical Computer Science
ISBN: 9781680831146
Category :
Languages : en
Pages : 206
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Book Description
This book deals mostly with impossibility results - lower bounds on what can be accomplished by algorithms. However, the perspective is unapologetically that of an algorithm designer. The reader will learn lower bound technology on a "need-to-know" basis, guided by fundamental algorithmic problems that we care about.
Author: Fabio Amodeo
Publisher:
ISBN:
Category :
Languages : en
Pages : 110
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Author: Eyal Kushilevitz
Publisher: Cambridge University Press
ISBN: 052102983X
Category : Computers
Languages : en
Pages : 209
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Book Description
Surveys the mathematical theory and applications such as computer networks, VLSI circuits, and data structures.
Author: Anup Rao
Publisher: Cambridge University Press
ISBN: 1108776019
Category : Computers
Languages : en
Pages : 271
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Book Description
Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.
Author: International Business Machines Corporation. Research Division
Publisher:
ISBN:
Category : Computer networks
Languages : en
Pages : 6
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Abstract: "A given Boolean function has its input distributed among many parties. The aim is to determine which parties to talk to and what information to exchange with each of them in order to evaluate the function while minimizing the total communication. This paper shows that it is possible to obtain the Boolean answer deterministically with only a polynomial increase in communication with respect to the information lower bound given by the nondeterministic communication complexity of the function."
Author: Matei David
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Communication complexity is an area of complexity theory that studies an abstract model of computation called a communication protocol. In a $k$-player communication protocol, an input to a known function is partitioned into $k$ pieces of $n$ bits each, and each piece is assigned to one of the players in the protocol. The goal of the players is to evaluate the function on the distributed input by using as little communication as possible. In a Number-On-Forehead (NOF) protocol, the input piece assigned to each player is metaphorically placed on that player's forehead, so that each player sees everyone else's input but its own. In a Number-In-Hand (NIH) protocol, the piece assigned to each player is seen only by that player. Overall, the study of communication protocols has been used to obtain lower bounds and impossibility results for a wide variety of other models of computation. Two of the main contributions presented in this thesis are negative results on the NOF model of communication, identifying limitations of NOF protocols. Together, these results consitute stepping stones towards a better fundamental understanding of this model. As the first contribution, we show that randomized NOF protocols are exponentially more powerful than deterministic NOF protocols, as long as $k \le n^c$ for some constant $c$. As the second contribution, we show that nondeterministic NOF protocols are exponentially more powerful than randomized NOF protocols, as long as $k \le \delta \cdot \log n$ for some constant $\delta
Author: Alfred J. Menezes
Publisher: Springer
ISBN: 3540384243
Category : Computers
Languages : en
Pages : 630
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Book Description
Crypto '90 marked the tenth anniversary of the Crypto conferences held at the University of California at Santa Barbara. The conference was held from August 11 to August 15, 1990 and was sponsored by the International Association for Cryptologic Research, in cooperation with the IEEE Computer Society Technical Committee on Security and Privacy and the Department of Computer Science of the University of California at Santa Barbara. 227 participants from twenty countries around the world. Crypto '90 attracted Roughly 35% of attendees were from academia, 45% from industry and 20% from government. The program was intended to provide a balance between the purely theoretical and the purely practical aspects of cryptography to meet the needs and diversified interests of these various groups. The overall organization of the conference was superbly handled by the general chairperson Sherry McMahan. All of the outstanding features of Crypto, which we have come to expect over the years, were again present and, in addition to all of this, she did a magnificent job in the preparation of the book of abstracts. This is a crucial part of the program and we owe her a great deal of thanks.
Author: Juraj Hromkovič
Publisher: Springer Science & Business Media
ISBN: 3662034425
Category : Computers
Languages : en
Pages : 347
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Book Description
The communication complexity of two-party protocols is an only 15 years old complexity measure, but it is already considered to be one of the fundamen tal complexity measures of recent complexity theory. Similarly to Kolmogorov complexity in the theory of sequential computations, communication complex ity is used as a method for the study of the complexity of concrete computing problems in parallel information processing. Especially, it is applied to prove lower bounds that say what computer resources (time, hardware, memory size) are necessary to compute the given task. Besides the estimation of the compu tational difficulty of computing problems the proved lower bounds are useful for proving the optimality of algorithms that are already designed. In some cases the knowledge about the communication complexity of a given problem may be even helpful in searching for efficient algorithms to this problem. The study of communication complexity becomes a well-defined indepen dent area of complexity theory. In addition to a strong relation to several funda mental complexity measures (and so to several fundamental problems of com plexity theory) communication complexity has contributed to the study and to the understanding of the nature of determinism, nondeterminism, and random ness in algorithmics. There already exists a non-trivial mathematical machinery to handle the communication complexity of concrete computing problems, which gives a hope that the approach based on communication complexity will be in strumental in the study of several central open problems of recent complexity theory.
