Lower Bounds For One Way Probabilistic Communication Complexity
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| Author | : University of Rochester. Dept. of Computer Science |
| Publisher | : |
| Total Pages | : 22 |
| Release | : 1992 |
| Genre | : Computer network protocols |
| ISBN | : |
Abstract: "We prove three different types of complexity lower bounds for the one-way unbounded-error and bounded-error error probabilistic communication protocols for boolean functions. The lower bounds are proved for arbitrary boolean functions in the common way in terms of the deterministic communication complexity of functions and in terms of the notion 'probabilistic communication characteristic' that we define. It is shown that for almost all boolean functions either the Yao's lower bound or the first or the third lower bound are more precise depending on the value of probability error.
| Author | : Troy Lee |
| Publisher | : Now Publishers Inc |
| Total Pages | : 152 |
| Release | : 2009 |
| Genre | : Computers |
| ISBN | : 1601982585 |
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 | : Juraj Hromkovič |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 347 |
| Release | : 2013-03-09 |
| Genre | : Computers |
| ISBN | : 3662034425 |
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.
| Author | : Andrzej Lingas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 716 |
| Release | : 1993-06-23 |
| Genre | : Computers |
| ISBN | : 9783540569398 |
The International Colloquium on Automata, Languages and Programming (ICALP) is an annual conference series sponsored by the European Association for Theoretical Computer Science (EATCS). It is intended to cover all important areas of theoretical computer science, such as: computability, automata,formal languages, term rewriting, analysis of algorithms, computational geometry, computational complexity, symbolic and algebraic computation, cryptography, data types and data structures, theory of data bases and knowledge bases, semantics of programming languages, program specification, transformation and verification, foundations of logicprogramming, theory of logical design and layout, parallel and distributed computation, theory of concurrency, and theory of robotics. This volume contains the proceedings of ICALP 93, held at LundUniversity, Sweden, in July 1993. It includes five invited papers and 51 contributed papers selected from 151 submissions.
| Author | : Satyanarayana V. Lokam |
| Publisher | : Now Publishers Inc |
| Total Pages | : 177 |
| Release | : 2009-07-20 |
| Genre | : Computers |
| ISBN | : 1601982429 |
We survey several techniques for proving lower bounds in Boolean, algebraic, and communication complexity based on certain linear algebraic approaches. The common theme among these approaches is to study robustness measures of matrix rank that capture the complexity in a given model. Suitably strong lower bounds on such robustness functions of explicit matrices lead to important consequences in the corresponding circuit or communication models. Many of the linear algebraic problems arising from these approaches are independently interesting mathematical challenges.
| Author | : Anupam Gupta |
| Publisher | : Springer |
| Total Pages | : 687 |
| Release | : 2012-07-20 |
| Genre | : Computers |
| ISBN | : 3642325122 |
This book constitutes the joint refereed proceedings of the 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012, and the 16th International Workshop on Randomization and Computation, RANDOM 2012, held in Cambridge, Massachusetts, USA, in August 2011. The volume contains 28 contributed papers, selected by the APPROX Program Committee out of 70 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 67 submissions. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
| Author | : Eyal Kushilevitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 209 |
| Release | : 2006-11-02 |
| Genre | : Computers |
| ISBN | : 052102983X |
Surveys the mathematical theory and applications such as computer networks, VLSI circuits, and data structures.
| Author | : Irit Dinur |
| Publisher | : Springer |
| Total Pages | : 750 |
| Release | : 2009-08-21 |
| Genre | : Computers |
| ISBN | : 3642036856 |
RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 13th workshop in the series following Bologna (1997), Barcelona (1998),Berkeley(1999),Geneva(2000),Berkeley(2001),Harvard(2002),Prin- ton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), and Boston (2008).
| Author | : Leslie Ann Goldberg |
| Publisher | : Springer |
| Total Pages | : 715 |
| Release | : 2011-08-05 |
| Genre | : Computers |
| ISBN | : 3642229352 |
This book constitutes the joint refereed proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011, and the 15th International Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, USA, in August 2011. The volume presents 29 revised full papers of the APPROX 2011 workshop, selected from 66 submissions, and 29 revised full papers of the RANDOM 2011 workshop, selected from 64 submissions. They were carefully reviewed and selected for inclusion in the book. In addition two abstracts of invited talks are included. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
| Author | : Anup Rao |
| Publisher | : Cambridge University Press |
| Total Pages | : 271 |
| Release | : 2020-02-20 |
| Genre | : Computers |
| ISBN | : 1108776019 |
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.
