Proceedings ArticleDOI
On non-linear lower bounds in computational complexity
Leslie G. Valiant
- pp 45-53
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TLDR
It is shown that the graph of any algorithm for any one of a number of arithmetic problems (e.g. polynomial multiplication, discrete Fourier transforms, matrix multiplication) must have properties closely related to concentration networks.Abstract:
The purpose of this paper is to explore the possibility that purely graph-theoretic reasons may account for the superlinear complexity of wide classes of computational problems. The results are therefore of two kinds: reductions to graph theoretic conjectures on the one hand, and graph theoretic results on the other. We show that the graph of any algorithm for any one of a number of arithmetic problems (e.g. polynomial multiplication, discrete Fourier transforms, matrix multiplication) must have properties closely related to concentration networks.read more
Citations
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MonographDOI
Computational Complexity: A Modern Approach
Sanjeev Arora,Boaz Barak +1 more
TL;DR: This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory and can be used as a reference for self-study for anyone interested in complexity.
Journal ArticleDOI
Applications of a Planar Separator Theorem
TL;DR: Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices, and this separator theorem in combination with a divide-and-conquer strategy leads to many new complexity results for planar graphs problems.
Proceedings ArticleDOI
An 0(n log n) sorting network
TL;DR: A sorting network of size 0(n log n) and depth 0(log n) is described, and a derived procedure (&egr;-nearsort) are described below, and the sorting network will be centered around these elementary steps.
Algebraic Complexity Theory.
TL;DR: Algebraic complexity theory as mentioned in this paper is a project of lower bounds and optimality, which unifies two quite different traditions: mathematical logic and the theory of recursive functions, and numerical algebra.
Journal ArticleDOI
A framework for solving vlsi graph layout problems
TL;DR: In this paper, a divide-and-conquer framework for VLSI graph layout is introduced, which is used to design regular and configurable layouts, to assemble large networks of processor using restructurable chips, and to configure networks around faulty processors.
References
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TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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