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Communication Complexity and Parallel Computing (Paperback, Softcover reprint of hardcover 1st ed. 1997)
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Communication Complexity and Parallel Computing (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Series: Texts in Theoretical Computer Science. An EATCS Series
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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."
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