" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

Fast matrix multiplication is one of the most fundamental problems in algorithm research.
The exponent of the optimal time complexity of matrix multiplication is usually denoted by ω …

This paper surveys the state of the art in sparse matrix research in January 1976. Much of
the survey deals with the solution of sparse simultaneous linear equations, including the …

Preprocessing, or data reduction, is a standard technique for simplifying and speeding up
computation. Written by a team of experts in the field, this book introduces a rapidly …

Recognizing text from natural images is a hot research topic in computer vision due to its
various applications. Despite the enduring research of several decades on optical character …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

Quantum field theory reconciles quantum mechanics and special relativity, and plays a
central role in many areas of physics. We developed a quantum algorithm to compute …

Secure multiparty computation (MPC) often relies on correlated randomness for better
efficiency and simplicity. This is particularly useful for MPC with no honest majority, where …

JA George has discovered a method, called nested dissection, for solving a system of linear
equations defined on an n=k*k square grid in O(n\logn) and space O(n^3/2) time. We …

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over
matrices Π∈ R m× n such that for any linear subspace W⊆ R n with dim (W)= d, P Π~ D (∀ …