Showing papers on "Sorting published in 1987"

Three partition refinement algorithms

Abstract: We present improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering. Our double lexical ordering algorithm uses a new, efficient method for unmerging two sorted sets.

Slowing down sorting networks to obtain faster sorting algorithms

Abstract: Megiddo introduced a technique for using a parallel algorithm for one problem to construct an efficient serial algorithm for a second problem. This paper provides a general method that trims a factor of O(log n) time (or more) for many applications of this technique.

Apparatus and method for multidimensional characterization of objects in real time

Abstract: A system for characterizing objects to be sorted in real time and making sorting decisions using lasers to excite fluorescing dyes used to tag objects such as cells which flow through the laser beam in a stream of conductive fluid. The scattered light and fluorescent light at various frequencies define a multidimensional space. These light characteristics are sensed and digitized. The data so gathered is buffered and then compared to a binary classification tree. The individual parameters cause a certain path through the binary decision tree to be taken while the cell is passing from the point in the stream where the light characteristics are gathered to a point where electrostatically charged electrodes deflect individual statically charged drops containing cells to be sorted into various sorting bins. When the decision tree has been traversed, the sorting decision for the drop containing the cell which had those parameters is done. This sorting decision is buffered until the time the drop reaches the charged electrodes. The sort decision is then accessed and used to properly charge the electrodes so that the drop is diverted into the proper bin.

Optimal Parallel Merging and Sorting Without Memory Conflicts

Abstract: A parallel algorithm is described for merging two sorted vectors of total length N. The algorithm runs on a shared-memory model of parallel computation that disallows more than one processor to simultaneously read from or write into the same memory location. It uses k processors where l ? k ? N and requires O(N/k + log k × log N) time. The proposed approach for merging leads to a parallel sorting algorithm that sorts a vector of length N in O(log2 k + N/k) log N) time. Because they modify their behavior and hence their running time according to the number of available processors, the two new algorithms are said to be self-reconfiguring. In addition, both algorithms are optimal, for k ? N/log2 N, in view of the ?(N) and ?(N log N) lower bounds on merging and sorting, respectively.

Sorting and selecting in rounds

Abstract: We present upper bounds for sorting and selecting the median in a fixed number of rounds. These bounds match the known lower bounds to within logarithmic factors. They also have the merit of being “explicit modulo expansion”; that is, probabilistic arguments are used only to obtain expanding graphs, and when explicit constructions for such graphs are found, explicit algorithms for sorting and selecting will follow. Using the best currently available explicit constructions for expanding graphs, we present the best currently known explicit algorithms for sorting and selecting in rounds.

Array architectures for iterative algorithms

Abstract: Regular mesh-connected arrays are shown to be isomorphic to a class of so-called regular iterative algorithms. For a wide variety of problems it is shown how to obtain appropriate iterative algorithms and then how to translate these algorithms into arrays in a systematic fashion. Several "systolic" arrays presented in the literature are shown to be specific cases of the variety of architectures that can be derived by the techniques presented here. These include arrays for Fourier Transform, Matrix Multiplication, and Sorting.

A time-space tradeoff for element distinctness

Abstract: In "A Time Space Tradeoff for Sorting on non-Oblivious Machines", Borodin et al. [B - 81] proved that to sort n elements requires TS = Ω(n2) where T=time and S=space on a comparison based branching problem. Although element distinctness and sorting are equivalent problems on a computation tree, the stated tradeoff result does not immediately follow for element distinctness or indeed for any decision problem. In this paper, we are able to show that TS=Ω(n3/2) for deciding element distinctness (or the sign of a permutation).

Factors governing the flow cytometric analysis and sorting of large biological particles.

Abstract: We have investigated the suitability of large flow cell tips for the flow cytometric analysis and sorting of large biological particles, including plant cells (pollen) and protoplasts. Using flow tips ranging in diameter from 79-204 micron, we have optimized conditions for the establishment of a stable hydrodynamic flow leading to accurate droplet production. We describe instrument modifications required for large particle sorting and demonstrate the use of these experimental conditions for the sorting to high purity of pollen and viable plant protoplasts possessing diameters as large as 95 micron. Our experiments have revealed a complex interaction among sorting efficiency, particle diameter, flow cell tip diameter and bimorphic crystal drive frequency. This interaction can be satisfactorily explained in terms of interference effects owing to phase differences between the particle-induced disturbance and the undulation driven by the bimorphic crystal.

Method of making up batches of small items, and an installation implementing the method

Abstract: The installation comprises a delivery conveyor (4) for delivering unit items in buckets (5). A station (3) injects unit items onto the delivery conveyor. A sorting conveyor (6) carries packs (8) corresponding to respective batches to be made up. The sorting conveyor is disposed relative to the delivery conveyor so as to establish at least one item transfer zone therebetween. A central control unit (10) ensure that desired coincidences occur between item-containing buckets (5) and packs (8) for receiving the items, with the control units controlling the transfer of items form the buckets to the packs. The invention is particularly applicable to making up batches of items in response to orders therefor.

Potential of Quality Sorting of Fruits and Vegetables Using Fluidized Bed Medium

Abstract: THIS report presents a review of literature on studies establishing the relationship between quality and density of fruits and vegetables, reviews the current concepts of fluidized bed medium (FBM), and presents potentials of using these concepts for density sorting. Results of initial experimentation with pecan pieces and pecan weevils larvae indicate separating and sorting, based on small density differences, may be possible using the newly developed FBM technique.

Optimal Sorting on Multi-Dimensionally Mesh-Connected Computers

Abstract: An algorithm is presented sorting N=n1n2...nr, r≧2, elements on an n1 × n2 × ... × nr mesh-connected array of processors within 2(n1+...+nr−1)+nr+0(n11−e+...+nr1−e), ɛ>0, data interchange steps. Hence this algorithm asymptotically matches the quite recently given lower bound for r-dimensional meshes. The asymptotically optimal lower bound of (2r/21/r) N1/r interchange steps can only be obtained on r-dimensional meshes withaspect ratio ni : nr=1 : 2 for all i=1,...,r−1. Moreover, for meshes with wraparound connections the slightly altered algorithm only need 1.5(n1+...+nr−1)+nr+0(n11−e+...+nr1−e) data interchange steps, which asymptotically is significantly smaller than the lower bound for sorting on meshes without wrap-arounds.

Device for counting and loading small items into containers

Abstract: A counting and batching device for items (24) such as tablets, capsules or caplets is faster than the electronic radial feeder counters, and is more easily adjustable for different quantities, sizes and shapes of items (24) than slat counters or disk counters. The device has a hopper (10) with an adjustable feed gate (12) and a first vibrator (20) to cause items (24) to flow from the feed gate (12). A V-guide sorting trough (22) is positioned beneath the feed gate (12) having a slot (28) at it's base to hold a single row of items (24), and a second vibrator (26) funnels items (24) into a single row moving along the slot (28). A moving belt (36) receives items (24) from the trough (22) and transports them in a single row between stationary guides (38) past an electronic counter (46) to a diverter (50) where a predetermined number of items (24) are diverted into at least two diverter streams. Loading positions (60) are provided under each diverter stream with provision for positioning and removing containers (62) independently into each loading position (60).

Lower bounds for sorting on mesh-connected architectures

Abstract: Lower bounds for sorting on mesh-connected arrays of processors are presented. For sorting N=n1 n 2...n r elements on an n 1×n2×... ×n r array 2(n 1+...+n r−1)+n r data interchange steps are needed asymptotically. For two dimensions these bounds are asymptotically best possible provided that n 1 and n 2 are powers of 2. In this case the generalized s 2-way merge sort of Thompson and Kung turns out to be asymptotically optimal. The minimal asymptotic bound of 2 √2N interchange steps can be obtained only by sorting algorithms suitable for √N/2×√2N meshes. For r≧3 dimensions an analysis of aspect-ratios also demonstrates that there exist mesh-connected architectures which are better suited for sorting than simple r-dimensional cubes.

Method of sorting goods and system therefor

Abstract: The invention relates to a method of sorting goods and a system therefor, and more particularly to an efficient method of sorting goods which arrive in the unit of items into groups which have been determined in advance in the order of delivery in a prescribed quantity so as to allow sequential loading of goods in a truck or the like in first-in-last-out manner depending on the item and quantity for a destination and/or a number of destinations, and to deal with changes in orders which frequently occur. The system applicable to this method includes plural assembling and storage conveyors (1A, 1B, 1C) for assembling goods in classified groups, a diverting conveyor (7, 17) which sorts out goods arrived in the unit of items into said assembling and storage (1A, 1B, 1C) and a control system (201-204) which controls said diverting conveyor (7,17) and said sorting out operation.

Simultaneous estimation of several percentiles

Abstract: In many simulation studies the performance of the modeled system is characterized only by mean values of the performance indices. However, the percentiles are more informative in sum marizing the performance. Several simultaneous percentiles, pre sented for example in the form of the boxplot, provide the analyst with better understanding of the system's behaviour.The simultaneous estimation of several percentiles is a cumber some task. The extended P2-algorithm proposed in this study significantly reduces the computation of the estimation. The algorithm simultaneously estimates several percentiles without storing and sorting the observations. Empirical validation studies indicate the algorithm can be used in simulation studies.

Problem-heap: A paradigm for multiprocesor algorithms

Abstract: The problem-heap paradigm has evolved through four years of experiments with the Multi-Maren multiprocessor Problem-heap algorithms have been formulated for a number of different tasks such as numerical problems, sorting, searching and optimization Although these tasks are very different, the analyses of the running times of all the problem-heap algorithms are very similar The problem-heap paradigm is illustrated by algorithms which have been implemented and analyzed using the Multi-Maren mulitiprocessor

The I/O Complexity of Sorting and Related Problems (Extended Abstract)

Abstract: We provide tight upper and lower bounds, up to a constant factor, for the number of accesses (I/Os) to secondary storage required for four sorting-related problems: sorting, the fast Fourier transform (FFT), permutation networks, and permuting records. The bounds hold both in the worst case and in the average case. Secondary storage is modeled as a magnetic disk capable of transfering P blocks each containing B records in a single time unit; the records in each block must be input from or output to B contiguous locations on the disk. We give two optimal algorithms for the problems, which are variants of merge sorting and distribution sorting. In particular we show for P=1 that the standard merge sorting algorithm is an optimal external sorting method. Our sorting algorithms use the same number of I/Os as does the permutation phase of key sorting, except when the internal memory size is extremely small, thus substantiating the popular adage that key sorting is not better. We also give a simpler and more direct derivation of a result due to Hong and Kung, which gives the FFT lower bound for the special case B=P=O(1).

The sorting of points along an algebraic curve

Abstract: The area of geometric modeling is concerned with the creation of computationally efficient models of solid physical objects to facilitate their design, assembly, and analysis. In a geometric modeling system, a solid such as a robot hand or a coffee cup is modeled by a collection of points, curves, and surfaces. The sorting of points along an algebraic curve is an operation that arises frequently during the creation and manipulation of geometric models. This thesis presents a thorough investigation of sorting, including an evaluation of the two conventional methods of sorting and the presentation of a new and superior method. A brute-force method of sorting is to trace along the curve, using Newton's method, and record the order in which the points are encountered. However, this method is inherently inefficient. A natural way to sort points along an algebraic curve is to use a rational parameterization of the curve. However, both of the main steps of this method, finding and solving a rational parameterization of the curve, can be difficult and expensive. Indeed, many curves do not even have a rational parameterization. We present a new method of sorting which is motivated by the observation that points on a convex segment of a curve can be sorted easily. The fundamental steps of this method are a decomposition of the curve into convex segments and a robust traversal of the curve by convex segments. This traversal is especially challenging in the neighbourhood of singularities. The points of inflection and singularities of the curve play a major role in the curve's decomposition into convex segments, which is a preprocessing step. We analyze the complexity of the three sorting methods and then present execution times for the three methods. The new method can sort points along any algebraic curve. Moreover, for those curves that can be sorted by all three of the sorting methods, the new method is usually much more efficient than the conventional methods. We illustrate important applications of sorting, including the intersection and display of geometric models.

Dynamic blocking for railyards: Part I. Homogeneous traffic

Abstract: This paper and its companion present a study of railroad classification yard strategies that allow for blocks of destinations to be assigned to classification tracks in different ways, depending on the time of day, week or month. With the same number of tracks, more classifications can be handled by this method. The paper examines homogeneous traffic; that is, traffic patterns where all blocks have the same amount of traffic, where cars for all blocks depart equally frequently from the yard and where the overall traffic flow does not change with time. The results represent the beginning of a better understanding of yard operations, which should be useful for designing new yards, planning expansions of existing ones and evaluating the impact of changes (planned and unplanned) on traffic patterns. The paper concentrates on two sorting strategies: sorting by train (perhaps the most commonly used strategy in the United States today), and triangular sorting. For both strategies, formulas are given for the minimum number of tracks, number of switches and for the total space requirements. For triangular sorting, the yard delay and total space depend on the time chosen between reswitches. These two measures of performance can be reduced if one is willing to accept a sorting effort slightly higher than minimum. The trade-off can be explored numerically. For sorting by train, yard delay and total space are not significantly affected by the sorting method; there is no such trade-off. It appears that sorting by train results in less work, delay and space requirements than triangular sorting, at least in most instances when either could be used. Triangular sorting, however, can be used when there are not enough tracks to allow sorting by train.

Thermoelectric Differences Used for Metal Sorting

Abstract: Thermoelectric or Seebeck effect devices are beginning to see wide-spread use in metal and alloy sorting and verification processes, prompting the recent approval of ASTM Practice for Thermo-electric Sorting of Electrically Conductive Materials (E 977). This paper briefly explores the history of its use and discusses the theory of the method, while focusing deeper attention on practical applications of the devices and areas of its limitations. Testing requirements, specific material separations and examples, variables, advantages, disadvantages, and traceability are highlighted.

The average complexity of deterministic and randomized parallel comparison sorting algorithms

Abstract: In practice, the average time of (deterministic or randomized) sorting algorithms seems to be more relevant than the worst case time of deterministic algorithms. Still, the many known complexity bounds for parallel comparison sorting include no nontrivial lower bounds for the average time required to sort by comparisons n elements with p processors (via deterministic or randomized algorithms). We show that for p ≥ n this time is Θ (log n/log(1 + p/n)), (it is easy to show that for p ≤ n the time is Θ (n log n/p) = Θ (log n/(p/n)). Therefore even the average case behaviour of randomized algorithms is not more efficient than the worst case behaviour of deterministic ones.

Method and device for sorting objects provided with a parameter, according to the value of this parameter

Abstract: In sorting an input file on the basis of parameter values of the objects, monotonically varying chains of the objects are formed first. In an inspection phase these chains are selected from which the selection objects will be found as k firsts of the selection objects in the output file, as well as the following selection object. Next, all the objects which on the basis of the parameter value need not function later than the (k+1)th selection object are incorporated in a sub-file, transported to a direct sorting machine and, if necessary, the chain formation is then repeated.

Apparatus for inspecting and sorting articles

Abstract: The invention is a device for sorting food products such as vegetables or fruit in accordance with their size, weight, and color or the presence of defects on them. In accordance with the device of the invention, a conveyor in the form of a plurality of rotatable rollers is employed for supporting the articles to be inspected and sorted. The articles are passed through an inspection zone where the articles are scanned in accordance with the sorting criteria of the apparatus. The articles are then sorted in accordance with in response to the determinations made at the inspection zone.

Memory intensive image sorter and method

Abstract: An image sorting system such as an airborne defense system for receiving and classifying enemy radar signals according to frequency, azimuth angle of arrival, etc. It employs a RAM that is addressed by the frequency and azimuth values of each received signal. If the addressed storage location in the RAM is empty, a number is assigned and stored there to represent the radar that is producing the received signals. The RAM represents a map of the aircraft's environment. Hash addressing, chaining of overlapping radar signals, pipelining to facilitate the blocking of superfluous pulse Doppler signals, etc. enable rapid reliable sorting and identification of hundreds of radar or other signals in the area.