Matrix rank and communication complexity
نویسندگان
چکیده
منابع مشابه
Matrix Rank in Communication Complexity
This lecture focuses on proving communication lower bounds using matrix rank. Similar to fooling sets and rectangle size bounds, the matrix rank technique also gives a lower bound on the number of monochromatic rectangles in any partition of X × Y but it does so in an algebraic way[1]. This makes algebraic tools available for proving communication lower bounds. We begin by solving the problem a...
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This paper concerns the open problem of Lovász and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We first give an example exhibiting the largest gap known. We then prove two related theorems.
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Def: A deterministic protocol computing a function f(x, y) is a binary tree T whose internal nodes specify which party speaks and the value of the bit they communicate, as a function of their input. The leaves of the tree are labelled with 0 or 1, in such a way that if Alice and Bob’s path through the tree given inputs (x, y) ends up in that leaf, the label on the leaf is f(x, y). The cost of s...
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This paper concerns the open problem of Lovasz and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We rst give an example exhibiting the largest gap known. We then prove two related theorems. y Extended Abstract appeared in FOCS 1994. subject "MAIL ME CLEAR", body "pub/eccc/ftpmail.txt" followed by an empty line, ...
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We prove that for every sign matrix A there is a deterministic communication protocol that uses O(corr1/4(A) log 2 rank(A)) bits of communication, where corr1/4(A) is the corruption/rectangle bound with error 1/4. This bound generalizes several of the known upper bounds on deterministic communication complexity, involving nondeterministic complexity, randomized complexity, information complexit...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2000
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00226-8