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Lower Bounds in Communication Complexity (Foundations and Trends in Theoretical Computer Science) by Troy Lee, Adi Shraibman is a nonfiction available to read on EtoBox.

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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. Definition 1.1. Let A be a sign matrix. The approximate rank of A with approximation factor α, denoted rank α (A), is rank α (A) = min B:1≤A[i,j]B[i,j]≤α rank(B).

Who reads Lower Bounds in Communication Complexity (Foundations and Trends in Theoretical Computer Science)?

Author

Troy Lee, Adi Shraibman

Publisher

Now Publishers Inc

Published

2007

Language

EN

ISBN

9780400000046

Category

nonfiction

Subjects

Computer Science, Science, Stem