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Given integers a and b with close to 2n bits each, the half-GCD of a and b is a 2×2 matrix [u v; u^' v^'] with determinant equal to -1 or 1 such that ua+vb=r and ...

For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

Parallel computing is the execution of a computer program utilizing multiple computer processors (CPU) concurrently instead of using one processor exclusively. Let T(n,1) be ...

The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices (u,v) of a directed or undirected graph. The length of the ...

Wolfram's iteration is an algorithm for computing the square root of a rational number 1<=r<4 using properties of the binary representation of r. The algorithm begins with ...

Newton's iteration is an algorithm for computing the square root sqrt(n) of a number n via the recurrence equation x_(k+1)=1/2(x_k+n/(x_k)), (1) where x_0=1. This recurrence ...

Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

The elliptic curve factorization method, abbreviated ECM and sometimes also called the Lenstra elliptic curve method, is a factorization algorithm that computes a large ...