Showing papers on "Sorting published in 1978"

Implementing Quicksort programs

Abstract: This paper is a practical study of how to implement the Quicksort sorting algorithm and its best variants on real computers, including how to apply various code optimization techniques. A detailed implementation combining the most effective improvements to Quicksort is given, along with a discussion of how to implement it in assembly language. Analytic results describing the performance of the programs are summarized. A variety of special situations are considered from a practical standpoint to illustrate Quicksort's wide applicability as an internal sorting method which requires negligible extra storage.

Selection and sorting with limited storage

Abstract: When selecting from, or sorting, a file stored on a read-only tape and the internal storage is rather limited, several passes of the input tape may be required. We study the relation between the amount of internal storage available and the number of passes required to select the Kth highest of N inputs. We show, for example, that to find the median in two passes requires at least Ω(N1/2) and at most O(N1/2 log N) internal storage. For probabilistic methods, Θ(N1/2) internal storage is necessary and sufficient for a single pass method which finds the median with arbitrarily high probability.

Optimal Sorting Algorithms for Parallel Computers

Abstract: The problem of sorting a sequence of n elements on a parallel computer with k processors is considered. The algorithms we present can all be run on a single instruction stream multiple data stream computer. For large n, each achieves an asymptotic speed-up ratio of k with respect to the best sequential algorithm, which is optimal in the number of processors used.

Fast parallel sorting algorithms

Abstract: A parallel bucket-sort algorithm is presented that requires time O(log n) and the use of n processors. The algorithm makes use of a technique that requires more space than the product of processors and time. A realistic model is used in which no memory contention is permitted. A procedure is also presented to sort n numbers in time O(k log n) using n1+1/k processors, for k an arbitrary integer. The model of computation for this procedure permits simultaneous fetches from the same memory location.

Computer controlled inspector/printer document inspection

Abstract: A document processor for transporting documents through a path, detecting flaws thereon by electronically scanning each side of the document, printing selectable indicia only on unflawed documents, and sorting and storing separately the flawed and unflawed documents. The electronically scanned information is compared with a master document stored in a computer memory. As a result of this comparison, outputs are provided from the computer which are indicative of a favorable or unfavorable comparison for controlling the printing and sorting functions.

The rebound sorter: an efficient sort engine for large files

Abstract: Sorting plays an increasingly important role in determining the overall performance of data base systems. Described is a new sorting scheme, called the rebound sort, implementable on a variety of technologies, e.g., magnetic bubbles and charge-coupled devices. The sort engine based on this new sorting scheme accepts as input a sequence of records, sorts them, and outputs the sorted records automatically. The actual sorting time is completely overlapped with the input/output time.

An Exchange: The Theory of Human Capital and the Earnings of Women: A Reexamination of the Evidence

Abstract: We propose a new approach to analyzing gender differences in wages. This approach identifies several alternative explanatory mechanisms to account for the sorting of women and men into different types of jobs that offer different levels of reward. ...

Automated Cell Sorting with Flow Systems

Abstract: The major successes of biochemistry and molular biology have derived from the isolation and characterization of macromolecules from complex solutions and structures. The analogous requirement in the field of cellular biology is for the preparation of pure populations of cells from organs and tissue culture. This ob jec­ tive is of primary importance in basic research of cellular differentiation and regula­ tion, as well as in applied areas such as clinical diagnosis and treatment. The same considerations apply to subcellular structures that extend from organelles or chromosomes to the ultimate structural limit of individual molecules, thereby bridging the gap with solution biochemistry. Cell separation is not a new problem nor has it been neglected in the past. Numerous methods exist for the bulk isolation of cells, including, for example, sedimentation, electrophoresis, or phase partitioning (134). In many instances, however, these methods lack sufficient selectivity. The techniques of automated cell analysis and sorting discussed here deal with the problem of heterogeneity by examining individual cells dispersed in suspension. Thus, the distributions of physical, structural, and functional properties of the population can be assessed and coupled in a logical manner with the sorting of desired cells for morphological examination or biologicallbioch emical studies. The flow systems designed for this purpose are capable of high speed (currently up to lOLI05 cells/sec) and a selectiv­ ity limited only by the nature of the reagents and physical signals used to differenti­ ate between the cellular subpopulations. In many instances, the sorting procedure can be carried out under conditions that insure preservation of viability and sterility. In fact, by eliminating debris and dead cells, overall viability can actually be increased. The duality of analysis and sorting cannot be overstressed. Although many flow instruments exist for analytical purposes alone and are of great utility. the

Statistical methods in algorithm design and analysis.

Abstract: : The use of statistical methods in the design and analysis of discrete algorithms is explored. Among the design tools are randomization, ranking, sampling and subsampling, density estimation, and 'cell' or 'bucket' techniques. The analysis techniques include those based on the design methods as well as the use of stochastic convergence concepts and order statistics. The introductory chapter contains a literature survey and background material on probability theory. In Chapter 2, probabilistic approximation algorithms are discussed with the goal of exposing and correcting some oversights in previous work. Some advantages of the proposed solution to the problems encountered are the introduction of a model for dealing with random problems, and a set of methods for analyzing the probabilistic behavior of approximation algorithms which permit consideration of fairly complex algorithms in which there are dependencies among the random variables in question. Chapter 3 contains many useful design and analysis tools such as those mentioned above, and several examples of the uses of the methods. Algorithms which run in linear expected time for a wide range of probabilistic assumptions about their inputs are given for problems ranging from sorting to finding all nearest neighbors in a point set in k dimensions. Empirical results are presented which indicate that the sorting algorithm, Binsort, is a good alternative to Quicksort under most conditions. Finally, Chapter 4 describes the uses of results from order statistics to analyze greedy algorithms and to investigate the behavior of parallel algorithms. Among the results reported here are general theorems regarding the distribution of solution values for optimization problems on weighted graphs.

Mail sorting machine

Abstract: The mail sorting machine of the present invention is capable of receiving a supply of envelopes in a magazine from which the individual envelopes are picked off in succession by means of a suction device operating in combination with a pair of conveying belts having a friction surface facing the incoming envelopes. The suction device acts through holes in the conveying belts to draw the lead envelope against the friction surface of the conveying belts for separation of this envelope from the rest of the supply. The separated envelope is then transferred to a read station where a reading device reads a sort code imprinted on the envelope. The envelope is then provided to the storage section of the machine where it is directed to its designated sorting bin. The storage section of the machine is provided with a plurality of diverter mechanisms which are arranged in pairs to form a guideway through which the envelopes are directed. As an envelope approaches its designated sorting bin, the diverter mechanism associated with this bin is activated. Activation of the diverter mechanism causes its deflector gate to be interposed within the guideway to direct the approaching envelope into the sorting bin associated with the deflector mechanism. Each sorting bin has a rib which runs along the floor of the bin to hold the envelopes in an offset position wherein the inherent vibratory motion of the machine causes the envelopes to be aligned in a neat stack. Each sorting bin is also equipped with a biasing plate which serves to keep the envelopes stored within the bin in a vertical plane.

Apparatus for controlling a coin sorting machine

Abstract: The jamming or misdistributing of coins inserted into a coin sorting machine in quick succession is prevented by providing detectors upstream of the coin distributing member and returning the coins if a secondly inserted coin passes the first detector before the first coin passes the second detector.

Conveyor sorting system

Abstract: A high speed conveyor sorting system includes a plurality of infeed conveyors coupled to an induction station including a merging conveyor for singulating articles from the infeed conveyor and inducting them onto a sorting conveyor. An operator actuated control system is employed for controlling the release mechanism of the induction station and diverters spaced along the sorting conveyor for discharging articles from the sorting conveyor onto preselected diverting conveyors spaced longitudinally along the sorting conveyor. The control system includes a portable training detector which is movably positioned near each of the divert locations such that the travel of an article from a predetermined reference point detector near the induction station to each of the divert locations can be accurately ascertained by counting pulses from a pulse position indicator associated with the conveyor during the travel interval of the article. Such information is stored in memory means of the control system and subsequently employed for the actuation of a diverter at preselected divert locations to effect accurate discharge of articles from the sorting conveyor to divert conveyors at the selected divert locations.

Document sorter utilizing cascaded sorting steps

Abstract: An automatic document sorter particularly suitable for sorting retail store coupons employs a plurality of relatively coarse sorting processes in cascade. The sorting processes sequentially sort the documents according to predetermined properties of the document, including codes, such as bar codes or the like; physical properties, such as size, thickness, color, reflectivity and opacity; the characteristics of the inscriptions on the face of the document; and any uniquely marked areas of the document face. Such a sorting hierarchy permits the documents to be sorted rapidly by reducing the precision required in each sorting step. The hierarchy also permits each document to be classified during each sorting step as falling into a particular class of documents in order to simplify subsequent sorting steps. If a property uniquely identifying the document is found during any one of the sorting steps, the processing is terminated at that point without completing the subsequent sorting steps.

Sorting on STAR

Abstract: This paper gives timing comparisons for three sorting algorithms written for the CDC STAR computer. One algorithm is Hoare's Quicksort, which is the fastest or nearly the fastest sorting algorithm for most computers. A second algorithm is a vector version of Quicksort that takes advantage of the STAR's vector operations. The third algorithm is an adaptation of Batcher's sorting algorithm, which makes especially good use of vector operations but has a complexity of N (log N)2 as compared to a complexity of N log N for the Quicksort algorithms. In spite of its worse complexity, Batcher's sorting algorithm is competitive with the serial version of Quicksort for vectors up to the largest that can be treated by STAR. Vector Quicksort outperforms the other two algorithms and is generally preferred. These results indicate that unusual instruction sets can introduce biases in program execution time that counter results predicted by worst-case asymptotic complexity analysis.

Stable Sorting in Asymptotically Optimal Time and Extra Space

Abstract: A stable sorting algonthm is one which does not permute the relative order of records which have equal keys. In The Art of Computer Programming, Vol 3, Exercise 5 5-3, Knuth poses the problem of finding a stable sorting algorithm which requires less than O(N ~2) time to sort N records, for arbitrary N, and which also requires no more than O(log N) bits of extra space (space in excess of that required to hold the N records) Section 1 shows that a stable sorting algorithm may be derived directly from a stable merging algorithm, and thereafter this paper is restricted to stable merging algorithms. Section 2 defines the concept of a contlguent, and shows that a conttguent-forming algonthm may be used as the basis for a stable merging algorithm. A class of contiguent-formmg algorithms which exhibit a space/time tradeoff is presented In the extremes, one algorithm in the class gives rise to a stable merge requiring O(N) time and O(N log N) bits of extra space, another algorithm reqmres O(N log N) Ume and O(log N) bits of extra space to merge Section 3 describes the Stable Kronrod Merge, which reqmres O(N) time and O(log N) bits of extra space, but is not applicable to all cases. Section 4, however, shows how the Stable Kronrod Merge may be combined with contlguent-formmg algorithms to yield a generally applicable class of stable merging algorithms. One algorithm in the class is shown to require O(N) time and O(log N) bRs of extra space to merge Finally, Section 5 places this work within the context of other work on this problem, both current and future

Asynchronous blueberry sorter

Abstract: The present invention relates to a high speed asynchronous fruit sorter for sorting various types of fruits, such as blueberries, according to maturity. Forming a part of the fruit sorter is an open wire type conveyor having a generally M-shaped profile extending transversely across so as to define a series of laterally spaced and longitudinally extending conveying channels. An illumination source is disposed below the conveyor about an area referred to as a sorting zone. Disposed over the conveyor in the vicinity of the sorting zone is an optical maturity sensing device that continuously derives a differential optical density reading for the underlying passing fruit, and this differential optical density reading is directly related to the maturity of the fruit and is directed to a maturity discriminator circuit. The maturity discriminator circuit is in turn coupled to an air injection sorting apparatus by a series of AND gates. An optical asynchronous detector apparatus is positioned about the sorting zone and is adapted to detect the leading edge of oncoming articles of fruit and to actuate the AND gates at a selected time after detection in order that the air ejection system can be appropriately actuated to transfer certain maturity level grades to an adjacent area for receiving that particular maturity grade.

Coin detecting device for a coin sorting machine

Abstract: A coin sorting device is provided for discriminating between a true coin of a desired denomination and a particular coin similar in configuration to the desired coin. The sorting device includes a coil adjacent the coin passage for detecting the passage of a coin and a detecting circuit which is finely tuned enough to discriminate between the two similar coins.

Simplified odd-even sort using multiple shift-register loops

Abstract: By using anN-loop shift-register structure called a uniform ladder,N records can be sorted by a simplified adaptation of the odd-even transposition-sort algorithm to finish in (N + 1)/2 loop times (periods) using (N − 1) comparators. The sorting can be overlapped with input/output; the percentage of unoverlapped sorting times is less than 20% of the total time with a single ladder, less than 6% using two ladders, and is zero with a sufficient number of ladders.

Coin sorting machine

Abstract: In a coin sorting machine of the type wherein a sorting coil for detecting the characteristics of a coin inserted into the machine is provided along a coin passage and the output signal of the coil is varied to thereby determine whether the inserted coin is true or false when the coin passes by the sorting coil, a coin sorting period is determined by detecting the position of the inserted coin rolling along the coin passage, and the inserted coin is sorted depending on whether or not a predetermined sorting signal is outputted during the coin sorting period.

Universal sorting apparatus

Abstract: A sorting apparatus universally applicable to any article sorting task without the necessity of changing a background member for each article type is characterized by first and second optically imposed "backgrounds" against which light reflected from the same portion of each article passing within a predetermined viewed area as defined by an optical frame is detected. Photodetectors associated with each "background" are operative to generate first and second electrical signal representations of the reflected light detected against each background. An electrical signal representative of the portion of the viewed area occupied by the article and functionally related to the difference between first and second signal representations is used to scale one of the first or second signals to provide a signal representation of the full-frame percentage reflectivity of the article. Additionally, a nulling circuit is operative while the articles are passing through the viewer to provide drift compensation.

Sorting installation esp. for semiconductor elements - uses distribution block between reject point and sorting compartments with fixed and adjustable channels

Abstract: The sorting installation is for electric circuit construction elements based on electric measuring values obtained by placing the construction elements into different sorting compartments positioned below the measuring or reject device for the elements. A distribution block is fitted between the throw out point for the construction elements and the sorting compartments which in the direction of fall of one construction element consists alternately of fixed elements and adjustable elements. Channels extend in the distribution elements for the guidance of the construction elements with the channels positioned in such a way that a channel in a fixed element can be brought into line one alter the other with several channels by the adjustment of the adjustable element positioned below.

Installation for sorting parcels - has loading points between groups of receptacles to increase capacity of closed loop conveyor without increasing its speed

Abstract: The installation is used for sorting parcels and comprises a conveyor (3) operating in a closed loop This can have a square or other configuration, depending on the number of loading points etc and has compartments (4) for holding one parcel each Several identical groups (A, B) of receptacles (1) are arranged around the conveyor length, each group having a loading point (5) between it and the adjacent group The unsorted parcels (2) are individually released onto the conveyor through a gate (6, 7) and the parcels are automatically offloaded

The generation of order statistics in digital computer simulation: A survey

Abstract: Order statistics are often needed in computer simulation. Common examples are quantile estimation and censored data test statistics. Methods for generating order statistics in various contexts are surveyed. Sorting and the use of histograms, the most general methods, are first discussed, followed by a method for non-identically distributed samples. Finally, the very powerful methods applicable to iid random variables are surveyed.