Communication Complexity and Parallel Computing

  • Juraj Hromkovič

Table of contents

  1. Front Matter
    Pages i-x
  2. Juraj Hromkovič
    Pages 1-6
  3. Juraj Hromkovič
    Pages 7-149
  4. Juraj Hromkovič
    Pages 151-240
  5. Juraj Hromkovič
    Pages 241-281
  6. Juraj Hromkovič
    Pages 283-315
  7. Back Matter
    Pages 317-339

About this book

Introduction

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.

Keywords

Boolean circuits Boolean functions Formale Sprachen Heuristics Kommunikationskomplexität Parallele Berechnungen Randomized and Approximation Algorithms VLSI VLSI-Schaltkreise algorithms comm communication complexity information

Authors and affiliations

  • Juraj Hromkovič
    • 1
  1. 1.Institut für Informatik und Praktische MathematikUniversität KielKielGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03442-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08185-9
  • Online ISBN 978-3-662-03442-2
  • Series Print ISSN 1862-4499
  • About this book