Showing papers on "Sorting published in 2000"

A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II

Abstract: Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN3) computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN2) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Because of NSGA-II's low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come.

On the sorting-complexity of suffix tree construction

Abstract: The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. We present a recursive technique for building suffix trees that yields optimal algorithms in different computational models. Sorting is an inherent bottleneck in building suffix trees and our algorithms match the sorting lower bound. Specifically, we present the following results. (1) Weiner [1973], who introduced the data structure, gave an optimal 0(n)-time algorithm for building the suffix tree of an n-character string drawn from a constant-size alphabet. In the comparison model, there is a trivial O(n log n)-time lower bound based on sorting, and Weiner's algorithm matches this bound. For integer alphabets, the fastest known algorithm is the O(n log n)time comparison-based algorithm, but no super-linear lower bound is known. Closing this gap is the main open question in stringology. We settle this open problem by giving a linear time reduction to sorting for building suffix trees. Since sorting is a lower-bound for building suffix trees, this algorithm is time-optimal in every alphabet mode. In particular, for an alphabet consisting of integers in a polynomial range we get the first known linear-time algorithm. (2) All previously known algorithms for building suffix trees exhibit a marked absence of locality of reference, and thus they tend to elicit many page faults (I/Os) when indexing very long strings. They are therefore unsuitable for building suffix trees in secondary storage devices, where I/Os dominate the overall computational cost. We give a linear-I/O reduction to sorting for suffix tree construction. Since sorting is a trivial I/O-lower bound for building suffix trees, our algorithm is I/O-optimal.

Algorithm Selection using Reinforcement Learning

Abstract: Many computational problems can be solved by multiple algorithms, with different algorithms fastest for different problem sizes, input distributions, and hardware characteristics. We consider the problem of algorithm selection: dynamically choose an algorithm to attack an instance of a problem with the goal of minimizing the overall execution time. We formulate the problem as a kind of Markov decision process (MDP), and use ideas from reinforcement learning to solve it. This paper introduces a kind of MDP that models the algorithm selection problem by allowing multiple state transitions. The well known Q-learning algorithm is adapted for this case in a way that combines both Monte-Carlo and Temporal Difference methods. Also, this work uses, and extends in a way to control problems, the Least-Squares Temporal Difference algorithm (LSTD(0)) of Boyan. The experimental study focuses on the classic problems of order statistic selection and sorting. The encouraging results reveal the potential of applying learning methods to traditional computational problems.

Wisconsin card sorting test: a new global score, with Italian norms, and its relationship with the Weigl sorting test.

Abstract: The Wisconsin card sorting test and the Weigl test are two neuropsychological tools widely used in clinical practice to assess frontal lobe functions. In this study we present norms useful for Italian subjects aged from 15 to 85 years, with 5-17 years of education. Concerning the Wisconsin card sorting test, a new measure of global efficiency (global score) is proposed as well as norms for some well known qualitative aspects of the performance, i.e. perseverative responses, failure to maintain the set and non-perseverative errors. In setting normative values, we followed a statistical methodology (equivalent scores) employed in Italy for other neuropsychological tests, in order to favour the possibility of comparison among these tests. A correlation study between the global score of the Wisconsin card sorting test and the score on the Weigl test was carried out and it emerges that some cognitive aspects are not overlapping in these two measures.

Sorting Out Sorts

Abstract: In this paper we analyze the theoretical implications of sorting data into groups and then running asset pricing tests within each group. We show that the way this procedure is implemented introduces a bias in favor of rejecting the model under consideration. By simply picking enough groups to sort into, the true asset pricing model can be shown to have no explanatory power within each group. THE COMMON PRACTICE OF SORTING STOCKS into groups to test asset pricing inferences began with the earliest tests of the CAPM (see Black, Jensen, and Scholes (1972)). Although the information loss from the sorting procedure has long been recognized (see Litzenberger and Ramaswamy (1979)), only recently have researchers begun to formally analyze the theoretical basis for doing such sorts. Lo and MacKinlay (1990) point out that if the sort is based on either a variable that is only known to be empirically correlated with returns or a variable measured within the sample, the test will contain a data-snooping bias. Liang (2000) argues that even when the sort is based on a variable estimated using prior data, measurement error in this variable can lead to false conclusions. In this paper we will focus on a different variation of the sorting technique analyzed in those papers. The empirical procedure that is the subject of this paper closely resembles the Black et al. (1972) grouping procedure. There is, however, one crucial distinction. Like the standard procedure, assets are sorted into groups using some criterion related to asset returns. However, rather than forming portfolios out of the groups, the tests are run within the groups. It is shown that this empirical procedure biases the results in favor of rejecting whatever asset pricing model is being tested. In particular, we show the following: 1. The explanatory power of the model will always be smaller within a

Sorting out access and neighbourhood factors in hedonic price modelling

Abstract: This paper investigates the analytical potential of factor analysis for sorting out neighbourhood and access factors in hedonic modelling using a simulation procedure that combines GIS technology and spatial statistics. An application to the housing market of the Quebec Urban Community (575,000 in population; study based on some 2,400 cottages transacted from 1993 to 1997) illustrates the relevance of this approach. In the first place, accessibility from each home to selected activity places is computed on the basis of minimum travelling time using the TransCAD transportation‐oriented GIS software. The spatial autocorrelation issue is then addressed and a general modelling procedure developed. Following a five‐step approach, property specifics are first introduced in the model; proximity and neighbourhood attributes are then successively added on. Finally, factor analyses are performed on each set of access and census variables, thereby reducing to six principal components an array of 49 individual attributes. Substituting the resulting factors for the initial descriptors leads to high model performances, controlled collinearity and stable hedonic prices, although remaining spatial autocorrelation is still detected in the residuals.

Mechanical Component Design for Multiple Objectives Using Elitist Non-dominated Sorting GA

Abstract: In this paper, we apply an elitist multi-objective genetic algorithm for solving mechanical component design problems with multiple objectives. Although there exists a number of classical techniques, evolutionary algorithms (EAs) have an edge over the classical methods in that they can find multiple Pareto-optimal solutions in one single simulation run. Recently, we proposed a much improved version of the originally proposed non-dominated sorting GA (we call NSGA-II) in that it is computationally faster, uses an elitist strategy, and it does not require fixing any niching parameter. In this paper, we use NSGA-II to handle constraints by using two implementations. On four mechanical component design problems borrowed from the literature, we show that the NSGA-II can find a much wider spread of solutions than classical methods and the NSGA. The results are encouraging and suggests immediate application of the proposed method to other more complex engineering design problems.

A method and system for sorting incident log data from a plurality of machines

Abstract: A method for sorting respective incident log data from a plurality of machines undergoing diagnostics is provided. The method allows for receiving incident log data comprising one or more incidents from the plurality of machines (e.g., 104 or 154) and for receiving operational parameter data from the plurality of machines (e.g., 156). The method further allows for executing a set of incident-authentication rules indicative of whether a received incident actually corresponds to a faulty condition or not (e.g., 158). An assigning step (e.g., 106 or 160) allows for assigning a predetermined incident severity rating to the respective incidents, and a processing (e.g., 164) step allows for processing the respective incidents based on their respective incident severity rating.

Selection of test nodes for analog fault diagnosis in dictionary approach

Abstract: In this paper, the selection of test nodes has been studied extensively and efficient techniques are proposed. Two broad categories of methods called inclusion methods and exclusion methods are suggested. Strategies are presented to select or delete a test node without affecting the diagnosis capabilities. Examples show that these strategies give a lesser number of test nodes some times. Starting from the fault-wise integer coded table of the test circuit, sorting is employed to generate valid sets and minimal sets. The order of computation of these methods is shown to depend linearly on number of test nodes. It is also proportional to (f log f) where "f" is the number of faults. This is much faster than well-known methods. The concept of minimal set of test nodes is new in analog circuit fault diagnosis. Polynomial time algorithms are proposed in this paper for the first time to generate such sets.

On the performance of BWT sorting algorithms

Abstract: In recent years lossless text compression based on the Burrows-Wheeler transform (BWT) has grown popular. The expensive activity during compression is sorting of all the rotations of the block of data to compress. Burrows and Wheeler (1994) describe an efficient implementation of rotation sorting but give little analysis of its performance. This paper addresses that need. We present the base algorithm using a more formal framework, describe two important optimisations not present in the original paper, and measure performance of the variants on a set of 14 files. For completeness, a tuned implementation of Sadakane's (1998) sorting algorithm was also tested. Merely measuring running times gives poor insight into the finer aspects of performance on contemporary machine architectures. We report measurements of instruction counts and cache misses for the algorithms giving a clearer picture of which variants perform well, and why.

Method and device for sorting parcels

Abstract: The invention relates to sorting items of mail in a plurality of sorting passes. In order not to have to read the address in each sorting pass and also not to have to print any machine-readable identification code on each item of mail, features characteristic of the items of mail are additionally determined during the first sorting pass and are stored together with distribution codes determined in the reading process. During the subsequent sorting passes only the characteristic features of the items of mail are measured and compared with the stored features. In the event of agreement, the item of mail is assigned the associated distribution code. A particular feed regime with defined orders ensures that in each case only n items of mail have to be compared, where n=maximum multiple delivery rate to be expected.

Towards a Theory of Cache-Efficient Algorithms

Abstract: We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O model, enables us to establish useful relationships between the cache complexity and the I/O complexity of computations. As a corollary, we obtain cache-optimal algorithms for some fundamental problems like sorting, FFT, and an important subclass of permutations in the single-level cache model. We also show that ignoring associativity concerns could lead to inferior performance, by analyzing the average-case cache behavior of mergesort. We further extend our model to multiple levels of cache with limited associativity and present optimal algorithms for matrix transpose and sorting. Our techniques may be used for systematic exploitation of the memory hierarchy starting from the algorithm design stage, and dealing with the hitherto unresolved problem of limited associativity.

Extension Of The Rough Set Approach To Multicriteria Decision Support

Abstract: The original version of the rough sets theory has proved to be particularly useful in the analysis of multiattribute classification problems under inconsistency following from information granulation, i.e. objects having the same description but belonging to different classes. It fails, however, when attributes with preference-ordered domains (criteria) have to be taken into account. In order to deal with problems of multicriteria decision analysis (MCDA), such as sorting, choice or ranking, the authors have extended the original rough sets theory in a number of directions. The main extension is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered decision classes in multicriteria sorting. Second extension was necessary to approximate preference relations in multicriteria choice and ranking problems; it requires substitution of the data table by a pairwise comparison table, where each row corresponds to a pair of actions described by bina...

Detection and sorting of neural spikes using wavelet packets.

Abstract: We propose a novel method for the detection and sorting of recorded neural spikes using wavelet packets. We employ the best basis via the Shannon's information cost function and local discriminant basis using mutual information. We demonstrate the efficiency of the method on data recorded in vitro from 2D neural networks. We show that our method is superior both in separation from noise and in identifying superimposed spikes.

Cell analysis and sorting apparatus for manipulation of cells

Abstract: A cell analysis and sorting apparatus is capable of monitoring over time the behaviour of each cell in a large population of cells. The cell analysis and sorting apparatus contains individually addressable cell locations. Each location is capable of capturing and holding a single cell, and selectively releasing that cell from that particular location. In one aspect of the invention, the cells are captured and held in wells, and released using vapor bubbles as a means of cell actuation. In another aspect of the invention, the cells are captured, held and released using electric fields traps.

Basic mechanisms of secretion: sorting into the regulated secretory pathway

Abstract: Targeting proteins to their correct cellular location is crucial for their biological function. In neuroendocrine cells, proteins can be secreted by either the constitutive or the regulated secretory pathways but the mechanism(s) whereby proteins are sorted into either pathway is unclear. In this review we discuss the possibility that sorting is either an active process occurring at the level of the trans-Golgi network, or that sorting occurs passively in the immature granules. The possible involvement of protein-lipid interactions in the sorting process is also raised. Key words: lipid rafts, regulated secretory pathway, secretion, sorting receptors, sorting signals, trans-Golgi network.

Minimizing communication in the bitonic sort

Abstract: This paper presents bitonic sorting schemes for special-purpose parallel architectures such as sorting networks and for general-purpose parallel architectures such as SIMD and/or MIMD computers. First, bitonic sorting algorithms for shared-memory SIMD and/or MIMD computers are developed. Shared-memory accesses through the interconnection network of shared memory SIMD and/or MIMD computers can be very time consuming. A scheme is introduced which reduces the number of such accesses. This scheme is based on the parity strategy which is the main idea of the paper. By reducing the communication through the network, a performance improvement is achieved. Second, a recirculating bitonic sorting network is presented, which is composed of one level of N/2 comparators plus an /spl Omega/-network of (log N-1) switch levels. This network reduces the cost complexity to O(N log N) compared with the O(N log/sup 2/ N) of the original bitonic sorting network, while preserving the same time complexity. Finally, a simplified multistage bitonic sorting network, is presented. For simplifying the interlevel wiring, the parity strategy is used, so N/2 keys are wired straight through the network.

Methods for encoding and sorting in vitro translated proteins

Abstract: Described herein are methods and reagents for encoding and sorting in vitro translated proteins.

On ordering fuzzy numbers

Abstract: At the heart of many statistical processing algorithms lies the concept of ordering a set of crisp numbers, either according to their own values (direct sorting), or according to the values of a second set of numbers (indirect sorting). In this paper we show how the concept of direct and indirect sorting may be generalized to fuzzy numbers. We present two techniques for doing this: one is based on fuzzy permutation matrices and the other is based on Zadeh's extension principle. In the final section of the article we use the new direct and indirect fuzzy sorting techniques to define two new fuzzy number ordered weighted average (OWA) operators.

Fuzzy Extension of the Rough Set Approach to Multicriteria and Multiattribute Sorting

Abstract: We consider a sorting (classification) problem in the presence of multiple attributes and criteria, called MA&C sorting problem. It concerns an assignment of some actions to some pre-defined and preference-ordered decision classes. The actions are described by a finite set of attributes and criteria. Both, attributes and criteria take values from corresponding domains, however, the domains of attributes are not preference-ordered, while the domains of criteria (scales) are totally ordered by preference relations. In order to construct a comprehensive preference model that could be used to support the sorting task, we are considering a preferential information of the decision maker (DM) in the form of assignment examples, i.e. exemplary assignments of some reference actions to the decision classes. The preference model being inferred from these examples is a set of “if..., then...” decision rules. The rules are derived from rough approximations of decision classes made up of reference actions. They satisfy conditions of completeness and dominance, and manage with possible ambiguity (inconsistencies) in the set of examples. Our idea of rough approximations involves two relations together: similarity, being a generalization of classic indiscernibility relation defined on attributes, and dominance relation defined on criteria. In this paper, we propose a fuzzy extension of the rough set approach to MA&C sorting problem.

A Unified Approach for Indexed and Non-Indexed Spatial Joins

Abstract: Most spatial join algorithms either assume the existence of a spatial index structure that is traversed during the join process, or solve the problem by sorting, partitioning, or on-the-fly index construction. In this paper, we develop a simple plane-sweeping algorithm that unifies the index-based and non-index based approaches. This algorithm processes indexed as well as non-indexed inputs, extends naturally to multiway joins, and can be built easily from a few standard operations. We present the results of a comparative study of the new algorithm with several index-based and non-index based spatial join algorithms. We consider a number of factors, including the relative performance of CPU and disk, the quality of the spatial indexes, and the sizes of the input relations. An important conclusion from our work is that using an index-based approach whenever indexes are available does not always lead to the best execution time, and hence we propose the use of a simple cost model to decide when to follow an index-based approach.

Method and apparatus for sorting documents into a pre-defined sequence

Abstract: A method and apparatus are provided for sorting documents. The documents are scanned to determine a characteristic of each document and then sorted in response to the scanned characteristic. In particular, a method is provided for multi-pass processing of documents. In accordance with one method, each document is assigned a logical sort number corresponding to the recipient of the document. The documents are then sorted in sequential order according to the logical sort numbers. A method is also provided that compares data scanned during a pass with data obtained during a previous pass to determine the recipient of the document. In addition a method is provided for marking the documents and sorting the documents so that the markings provide indicators of pre-defined groups of documents.