Divide and conquer algorithms

About: Divide and conquer algorithms is a research topic. Over the lifetime, 2407 publications have been published within this topic receiving 39441 citations.

A simple and efficient estimator for hyperbolic location

Abstract: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed. The approach is noniterative and gives an explicit solution. It is an approximate realization of the maximum-likelihood estimator and is shown to attain the Cramer-Rao lower bound near the small error region. Comparisons of performance with existing techniques of beamformer, spherical-interpolation, divide and conquer, and iterative Taylor-series methods are made. The proposed technique performs significantly better than spherical-interpolation, and has a higher noise threshold than divide and conquer before performance breaks away from the Cramer-Rao lower bound. It provides an explicit solution form that is not available in the beamforming and Taylor-series methods. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. >

The Multiplicative Weights Update Method: A Meta-Algorithm and Applications

Abstract: Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analyses are usually very similar and rely on an exponential potential function. In this survey we present a simple meta-algorithm that unifies many of these disparate algorithms and derives them as simple instantiations of the meta-algorithm. We feel that since this meta-algorithm and its analysis are so simple, and its applications so broad, it should be a standard part of algorithms courses, like "divide and conquer."

Algorithmic skeletons : structured management of parallel computation

Abstract: This book introduces a new approach to the design and implementation of software systems which will help users of large scale parallel systems coordinate many concurrent activities toward a single goal It assesses the strengths an weaknesses of this approach with existing alternativesCole's system proposes a selection of independent algorithmic skeletons, each of which describes the structure of a particular style of algorithm The user must describe a solution to a problem as an instance of the appropriate skeleton The implementation task is simplified by the fact that each skeleton may be considered independently, in contrast to the monolithic programming interfaces of existing systems at a similar level of abstractionThe book describes four skeletons based on the notions of fixed degree divide and conquer, task queues, iterative combination, and clustering Each is introduced in terms of the abstraction it presents to the user Implementation on a square grid of autonomous processor memory pairs is considered and examples of problems which could be solved in terms of the skeleton are presentedMurray I Cole is a Lecturer in the Computing Science Department of the University of Glasgow "Algorithmic Skeletons" is included in the series Research Monographs in Parallel and Distributed Computing, Copublished with Pitman Publishing,

Multidimensional divide-and-conquer

Abstract: Most results in the field of algorithm design are single algorithms that solve single problems. In this paper we discuss multidimensional divide-and-conquer, an algorithmic paradigm that can be instantiated in many different ways to yield a number of algorithms and data structures for multidimensional problems. We use this paradigm to give best-known solutions to such problems as the ECDF, maxima, range searching, closest pair, and all nearest neighbor problems. The contributions of the paper are on two levels. On the first level are the particular algorithms and data structures given by applying the paradigm. On the second level is the more novel contribution of this paper: a detailed study of an algorithmic paradigm that is specific enough to be described precisely yet general enough to solve a wide variety of problems.

Prefix sums and their applications

Abstract: "Experienced algorithm designers rely heavily on a set of building blocks and on the tools needed to put the blocks together into an algorithm. The understanding of these basic blocks and tools is therefore critical to the understanding of algorithms. Many of the blocks and tools needed for parallel algorithms extend from sequential algorithms, such as dynamic-programming and divide-and-conquer, but others are new. This paper introduces one of the simplest and most useful building blocks for parallel algorithms: the all-prefix-sums operation. The paper defines the operation, shows how to implement it on a P-RAM and illustrates many applications of the operation.In addition to being a useful building block, the all-prefix-sums operation is a good example of a computation that seems inherently sequential, but for which there is an efficient parallel algorithm."