Fast Sorting Algorithm Research Articles

A novel state selection technique for power system reliability evaluation

Only credible system states up to a certain contingency level are usually investigated in the reliability evaluation of power systems. The probabilities of some high level outage states may be larger than those of some low level outage states since system components may be not identical. The number of these high level outages with relatively large probabilities can be very large in a practical system. Their impact on system reliability can be very significant. However these high level outage states are ignored in the existing state selection techniques. The problem can be solved by the novel state selection technique proposed in this paper. In this technique, a pre-process has been used to arrange system components based on their availabilities in ascending order. A fast sorting algorithm (FSA) has been derived to quickly select the required number of the system states in descending probability order with the minimum number of computations and comparisons. For the given number of system states to be considered, the accuracy of reliability indices obtained using the proposed technique is much higher than that using the existing techniques. On the other hand, for the same accuracy the number of system states to be evaluated using the proposed technique is much less than that using the existing technique. The proposed technique has been illustrated by the IEEE-RTS.

A fast sorting algorithm for large volume datasets

We introduce a new and efficient sorting technique, referred to as BT-Sort after the Bayer-balanced Tree (B-Tree) method. It is fast and parsimonious on usage of memory and scratch space, and is thus deemed very attractive for sorting very large datasets. One property of BT-Sort is that it minimizes the use of random I/O needed for accessing the scratch disk, regardless of the size of datasets being sorted. Furthermore, it uses sequential I/O to/from scratch disks in a very efficient way, and does not require large memory. For example, with such features, sorting 1.2 TB of input shot gathers into ordered common-midpoint gathers with BT-Sort would require only three days using four computing nodes (each of say 32 GB, 375 MHz RISC architecture), whereas the same exercise would typically require six to eight weeks to complete using conventional sorting techniques. From a seismic operational point of view, a rapid increase in seismic traces might result in altering some of the algorithms needed in the processing. Taking Saudi Aramco as an example, the current level of seismic-data acquisition there stands at 10 seismic crews, eight of which are 3D-seismic. The average count on these crews is about 2500 channels per crew. With an average daily production rate of some 2000 vibration points, the corresponding volume of seismic data flowing into processing is some 40 million traces per day. Consequently, some of the processing algorithms are being constantly updated in order to handle these massively increasing seismic volumes. Frequent sorting of seismic data into various domains (e.g. common-midpoint, common-receiver, etc.) has traditionally been avoided mainly because of the lack of efficient sorting algorithms. In the extreme case, sorting very large datasets with only limited computer resources (a few GB of memory) is a hugely inefficient task as the operation could take months to complete. As a compromise, geophysicists at times have opted to reformulate some existing processing algorithms such that seismic data would be kept in a certain preferred order throughout the processing sequence. One example was the reformulation of the dip-moveout operator by Biondi and Ronen (1987), so that it can be applied directly to recorded shot profiles instead of common-offset gathers if data cannot be sorted to common offsets (due to cost or other practical reasons), thereby avoiding the cost-prohibitive sorting process. Another, even worse shortcoming lies in the inability to apply some domain-specific processing algorithms, such as those for noise suppression and Radon multiple removal that require implementation in the common-receiver and common-midpoint (CMP) domains, respectively. In the case of (PRT) to normal-moveout-corrected CMP gathers, for example, geophysicists have attempted to speed up the process by optimizing the PRT operator (Kelamis and Chiburis 1992; Beylkin and Vassiliou 1998); this multiple elimination process in its entirety can benefit even further if data were sorted from shot to CMP gathers in a much faster way such as that proposed here. Unfortunately, lack of a fast sort may inevitably force the seismic data to suffer from unnecessary noisy contaminations if the expensive (slow) sort is to be avoided (Al Dossary et al. 1998). When using conventional (quick or heap) sorting algorithms, one may in theory estimate the cost (in terms of the number of operations to be performed) as N log2 N (Press et al. 1988), where N is the number of traces. On this basis, 500 million traces, for example, would require about 15 billion operations to sort them. In practice, however, such an implementation is more complicated than simply coping with a formidable number of operations. Specifically, the entire dataset should physically reside in memory (internal sorting) in a stand-alone system, a task most computer-hardware configurations cannot support.

Fast sorting algorithms on a linear array with a reconfigurable pipelined bus system

We present two fast algorithms for sorting on a linear array with a reconfigurable pipelined bus system (LARPBS), one of the recently proposed parallel architectures based on optical buses. In our first algorithm, we sort N numbers in O(log N log log N) worst-case time using N processors. In our second algorithm, we sort N numbers in O((log log N)/sup 2/) worst-case time using N/sup 1+/spl epsi// processors, for any fixed /spl epsi/ such that 0 < /spl epsi/ < 1. Our algorithms are based on a novel deterministic sampling scheme for merging two sorted arrays of length N each in O(log log N) time on an LARPBS with N processors. To our knowledge, the previous best sorting algorithm on this architecture has a running time of O((log N)/sup 2/) using N processors.

Fast Polyhedral Cell Sorting for Interactive Rendering of Unstructured Grids

Direct volume rendering based on projective methods works by projecting, in visibility order, the polyhedral cells of a mesh onto the image plane, and incrementally compositing the cell’s color and opacity into the final image. Crucial to this method is the computation of a visibility ordering of the cells. If the mesh is “well‐behaved” (acyclic and convex), then the MPVO method of Williams provides a very fast sorting algorithm; however, this method only computes an approximate ordering in general datasets, resulting in visual artifacts when rendered. A recent method of Silva et al. removed the assumption that the mesh is convex, by means of a sweep algorithm used in conjunction with the MPVO method; their algorithm is substantially faster than previous exact methods for general meshes.In this paper we propose a new technique, which we call BSP‐XMPVO, which is based on a fast and simple way of using binary space partitions on the boundary elements of the mesh to augment the ordering produced by MPVO. Our results are shown to be orders of magnitude better than previous exact methods of sorting cells.

Sorting Data Sets and Computing Medians for Skewed Distributions

Clusters derived from data sets require meaningful interpretation, for which standard statistical packages, major spreadsheets, numerical computation texts, as well as the specialized Journal of Classification provide little help. Interpretation can be made from a profile of summary scores, means, or medians, representing distributions of scores. For such a profile, medians are preferable to means where the distributions are highly skewed. To automate computation of medians in either ordered or unordered sets of scores, a program, SHELMEDS.BAS, was written incorporating the very fast Shell-Metzner sort algorithm and routines for odd or even numbers of scores.

How Good Sorts Go Bad

This article presents techniques for generating permutations of 1. N that yield the worst case for several fast sorting algorithms. Specifically, we investigate an improved version of Quicksort, TreeSort, recursive and iterative versions of MergeSort, and HeapSort. In each case, a worst‐case permutation is developed. Such permutations are needed to analyze the worst‐case, run‐time behavior of these sorting algorithms. The results of comparing the worst‐case and average‐case performance are reported, and these results confirm the Big‐O analysis.

Three-dimensional direct particle simulation on the connection machine

This paper presents the algorithms necessary for an efficient data parallel implementation of a 3D particle simulation. In particular, a general master/slave algorithm and a fast sorting algorithm are described and the use of these algorithms in a particle simulation is outlined. A particle simulation using these algorithms has been implemented on a 32768 processor Connection Machine that is capable of simulating over 30 million particles at an average rate of 2.4-microsec/particle/step. Results are presented from the simulation of flow over an Aeroassisted Flight Experiment geometry at 100 km altitude.

An Adaptive Method for Unknown Distributions in Distributive Partitioned Sorting

Distributive Partitioned Sort (DPS) is a fast internal sorting algorithm which rung in O(n) expected time on uniformly distributed data. Unfortunately, the method is biased toward such inputs, and its performance worsens as the data become increasingly nonuniform, such as with highly skewed distributions. An adaptation of DPS, which estimates the cumulative distribution function of the input data from a randomly selected sample, was developed and tested. The method runs only 2-4 percent slower than DPS in the uniform case, but outperforms DPS by 12-13 percent on exponentially distributed data for sufficiently large files.

A fast sorting algorithm, a hybrid of distributive and merge sorting

A fast sorting algorithm, a hybrid of distributive and merge sorting

A fast sorting algorithm

A fast sorting algorithm

Fast sorting algorithms in the internal memory

Fast sorting algorithms in the internal memory