This paper gives an overview of faster algorithms known for sorting and searching on the word RAM, many of which were developed within the last few years.Expand

We show that a unit-cost RAM with a word length of bits can sort integers in the range in time, for arbitrary ! , a significant improvement over the bound of " # $ achieved by the fusion trees of… Expand

Kant 27] proved that a canonical ordering or a 4-connected triangular planar graph is possible, in which every vertex v k has out(v k) 2, which decreases the width of a visibility representation by a factor 2, and Nummenmaa showed a linear time algorithm for constructing a visibility representations.Expand

The algorithm is closer to optimality than all previous algorithms for the stated problem in the stated model, and the third result matches the operation count of the best known sequential algorithm.Expand

It is shown that the component tree for an undirected network can be constructed in deterministic linear time and space with a simple algorithm, to be contrasted with a complicated and impractical solution suggested by Thorup.Expand

A simple randomized scheme that uses n log e+log log u+o(n+loglog u) bits and has constant evaluation time and O(n + log log u) expected construction time is presented.Expand

In the course of solving the duplicate-grouping problem, a new universal class of hash functions of independent interest is described, and it is shown that both of the foregoing problems can be solved by randomized algorithms that useO(n) space and finish inO( n) time with probability tending to 1 asngrows to infinity.Expand

We study the problem of generating random permutations, i.e., of drawing random elements from the uniform distribution over the set of all permutations of a finite set. Our results are the following,… Expand