Optimal Randomized Algorithms for Local Sorting and Set-Maxima

Global and Local Optimization Algorithms for Optimal Signal Set Design

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here we consider the application of several optimization algorithms, both global and local, to this problem. The most promising results are obtained when special-purpose sequential quadratic programming (SQP) a...

Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms

We assume a parallel RAM model which allows both concurrent reads and concurrent writes of a global memory. Our main result is an optimal randomized parallel algorithm for INTEGER SORT (i.e., for sorting n integers in the range [1; n]). Our algorithm costs only logarithmic time and is the rst known that is optimal: the product of its time and processor bounds is upper bounded by a linear functi...

Derivation of Randomized Sorting and Selection Algorithms

In this paper we systematically derive randomized algorithms (both sequential and parallel) for sorting and selection from basic principles and fundamental techniques like random sampling. We prove several sampling lemmas which will find independent applications. The new algorithms derived here are the most efficient known. From among other results, we have an efficient algorithm for sequential...

Optimal Parallel Randomized Algorithms for . . .

Optimal Randomized Comparison Based Algorithms for Collision

We consider the well known problem of finding two identical elements, called a collision, in a list of n numbers. Here, the (very fast) comparison based algorithms are randomized and will only report existing collisions, and do this with (small) probability p, the success probability. We find a trade-off between p and the running time t, and show that this trade-off is optimal up to a constant ...