A provably fast linear-expected-time maxima-finding algorithm

A volume first maxima-finding algorithm

The maxima-finding is a fundamental problem in computational geometry with many applications. In this paper, a volume first maxima-finding algorithm is proposed. It is proved that the expected running time of the algorithm is N + o(N) when choosing points from CI distribution, which is a new theoretical result when the points belong to d(>2) dimensional space. Experimental results and theoretic...

Implementation of a Linear Expected-Time Algorithm for Finding Connected Components

We describe a robust and efficient implementation of the Karp and Tarzan [4] algorithm for finding the connected components of an undirected graph. The algorithm achieves to find the connected components of a graph G = (V,E) in O(|V|) expected time. The implementation of the algorithm (called GCOMPONENTS) is based on the LEDA library of efficient data types and algorithms [5,6,7]. This is the f...

A Practical Shortest Path Algorithm with Linear Expected Time

Linear Expected Time of a Simple Union-Find Algorithm

This paper presents an analysis of a simple tree-structured disjoint set Union-Find algorithm, and shows that this algorithm requires between n and 2n steps on the average to execute a sequence of n Union and Find instructions, assuming that each pair of existing classes is equally likely to be merged by a Union instruction. Union-Find algorithms are useful in the solution to a number of proble...

AN ALGORITHM FOR FINDING THE STABILITY OF LINEAR TIME-INVARIANT SYSTEMS

The purpose of this paper is to show that the ideas and techniques of the classical methods of finding stability, such as the criteria of Leonhard and Nyquist, can be used to derive simple algorithm to verify stability. This is enhanced by evaluating the argument of the characteristic equation of a linear system in the neighbourhood of the origin of the complex plane along the imaginary axis