Showing papers on "Sorting published in 1972"

Sorting Using Networks of Queues and Stacks

Abstract: Inspired by Knuth [2, p. 234], we wish to consider the following problem: Suppose we are presented with the layout of a railroad switchyard (Figure 1 ). I f a train is driven into one end of the yard, what rearrangements of the cars may be made before the train comes out the other end? In order to get a handle on the problem, we must introduce some formalization. A switchyard is an acyclic directed graph, with a unique source and a unique sink (Figure 2). Each vertex represents a siding. The vertex/siding is assumed to have indefinite storage space and may be a stack, a queue, or a deque of some sort (see Knuth [2, p. 234]). A stack is a siding which has the property tha t the last element inserted is the first to be removed. A queue has the proper ty tha t the first element inserted is the first to be removed. In the switchyard, the sidings associated with the source and sink are assumed to be queues. Suppose a finite sequence of numbers s = (sl, s2, • • • , sn) is placed in the source queue of a switchyard (Figure 3). We may rearrange s by moving the elements of s through the switchyard. At each step, an element is moved from some siding to another siding along an arc of the switchyard. After a suitable number of such moves, all elements will be in the sink queue. I f they are in order, smallest to largest, we have sorted the sequence s using the switchyard. We wish to analyze the sequences s which may be sorted in a switchyard Y. We lose nothing in our formalism by allowing storage only on the vertices, and not on the arcs of the switchyard. We ignore questions concerning the finite size of the sidings; assuming small sidings complicates the problem considerably. A circuit in the switchyard will allow us to sort any sequence; thus we do not allow circuits. Having established our model, we proceed to discover its properties.

Ink jet printing

Abstract: Several basically different nonimpact printing processes have been developed in the last several years using modulated or deflected ink jets. This review paper describes these processes, which are also applicable to the accurate dispensing of fluids, particle sorting, the generation of uniform droplets for research purposes, and other applications.

Shellsort and sorting networks

Abstract: : Shellsort is a particular method of sorting data on digital computers. Associated with each variant of Shellsort is a sequence of integers that characterizes that variant. In the paper the author answers some open questions about the speed of Shellsort with certain characteristic sequences, and suggests a novel application of Shellsort, namely to sorting networks. Shellsort with any characteristic sequence that approximates a geometric progression and that has short coprime subsequences through takes O(n sup 3/2) units of time. For any sequence that approximates a geometric progression with an integer common ratio, this bound is the best possible. However, if the sequence consists of the descending sequence of positive integers less than n and having only 2 and 3 as prime factors, then Shellsort takes only O(n log squared n) units of time. Sorting networks based on Shellsort with this sequence operate approximately 1.5 times as fast as with previous methods.

A sorting problem and its complexity

Abstract: A technique for proving min-max norms of sorting algorithms is given. One new algorithm for finding the minimum and maximum elements of a set with fewest comparisons is proved optimal with this technique.

Article aligning apparatus

Abstract: An induction apparatus includes a pair of induction stations having input ends coupled to feed conveyors for transferring articles to the induction stations. Each station includes an induction line extending between an input conveyor and a sorting conveyor and inter-secting the sorting conveyor at an acute angle. The induction line of each induction station includes a powered conveyor, an indexing station and a variable speed feed conveyor controlled to induct cartons onto predetermined trays of the sorting conveyor in a synchronous manner. Aligning means are provided for finally aligning cartons on the trays once they are inducted thereon.

Sorting by natural selection

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Automatic Sorting of Signals in Shift Reagent Spectra

Abstract: This communication shows a simple algorithm for the automatic sorting of signals in shift reagent spectra with an implicit plot of chemical shifts vs improved shift reagent coordinates

An Improved Lower Bound for Sorting Networks

Abstract: The minimum number of comparators S(N) required by an N-input sorting network is bounded below by S(N) ? N[log 2 (N) - 1] + 0(1), as a consequence of the theorem S(N) ? S(N - 1) + [log 2 (N)].

Binless sorting apparatus

Abstract: This invention relates to a web sorting apparatus for receiving and collating sheets from a copying machine. Roll members having a pair of belt members wound thereon are rotated in first one direction to separate and load copies of sheet No. 1 and then the opposite direction to separate and load copies of sheet No. 2. While sheets are not in the loading area they are trapped between layers of a belt on one of the rolls for temporary storage and protection. The operation is repeated until all the pages are loaded between the belt members. At this time the belts separate to unload the collated sets of copies into a receiving tray. By virtue of two separate paths, to the loading station simplex and duplex sorting modes of operation is accomplished.

Method for automatically sorting block-type objects of different categories and apparatus therefor

Abstract: A lumber or like objects sorting apparatus is arranged to be operative so that at the time block-type objects of various different categories are loaded, at different sites, on a single main conveyor in succession without the objects being superposed one upon another, the information of both the categories of the objects to be sorted and the positions at which the objects were loaded on the main conveyor is registered in a memorizer, and that, as the objects are carried along on this conveyor, they are unloaded - at the signal coming from the memorizer - off the main conveyor when these objects arrive at their respective designated positions of removal for the respective categories. Thus, it is possible to automatically deliver the sorted objects at their designated positions of removal, i.e., onto the designated classified individual receptacles.

Handling and sorting devices

Abstract: Apparatus and method for handling or sorting articles of magnetic material by magnetomotive means. The articles are fed to a guide across which a magnetic flux is maintained between a pair of pole pieces of a magnetomotive means; the magnetic flux increasing in density along the guide so as to separate and move the articles along the guide in the direction of increasing magnetic flux density.

Device for sorting carpet rolls

Abstract: A device for sorting rolls of carpet. The carpet roll is transferred by a carrier from a loading location to a second selected location where the carpet roll is dumped by the carrier into a waiting depository.

On the Realization of Functions in N-Valued Logic

Abstract: A system of N-valued logic that is based on three basic sets of functions is described. These functions are selected so that they are easy to realize physically with conventional electronic circuitry. Furthermore, the system is functionally complete.

Method and apparatus for sorting and cleaning bottles

Abstract: Bottles are loaded onto an automated sanitary table having a cleaning device thereon to which the bottles are channeled seriatim. The table serves to orientate the bottles in a line leading to the entrance of the cleaning device. The cleaning device is of the rotating wheel type wherein upright bottles are continuously fed into one side of the wheel, inverted and cleaned, and deposited upright on the other side of the wheel. The vertical plane of the wheel is located at approximately a 45 DEG angle with respect to the entry and exit line of the bottles, which allows the bottles to travel a path defining an obtuse angle as they enter and leave the device, thereby greatly increasing the efficiency of bottle entry and exit and allowing faster operation of the cleaning wheel.

Clutch-operated diverter for sorting system

Abstract: Diverter gates for diverting lumber, logs or similar products from an infeed conveyor to preselected sorting stations are operated through one-revolution or partial-revolution clutches. Clutch engagement and disengagement is synchronized to the movement of the infeed conveyor in a manner so that a diverter gate opens and closes when a piece to be diverted is in predetermined positions relative to such gate. The drives for the gates and infeed conveyor are interconnected in a manner so that variations in infeed speeds result in corresponding variations in the speed at which the gates are opened and closed, thereby enabling high-speed sorting.

Psychological significance in personal and supplied construct systems: A defining experiment

Abstract: An implication was examined of three assumptions of Personal Construct Theory. Personal and supplied construct systems were compared for their capacity to account for 34 subjects' behaviour in an independent sorting task. It was found that either construct system tended to account for a significant amount of the variance in sorting behaviour, but that more was accounted for by personal Construct systems. Observations were made on the way in which this phenomenon varied between subjects, sub-tasks, and parts of construct systems. The assumptions examined were held to be relevant to Social perception and cognitive theories.

A decomposition algorithm for integer programming problems with many columns

Abstract: One of the major computational problems of IP is dealing with the large number of variables (also called act iv i t ies or columns) arising in many applications. In addition to core storage l imitat ions, there is the d i f f i cu l t y of greatly increasing computer solution time for a branch and bound search as a function of the number of variables in the search. A related d i f f i cu l t y for branch and bound is the uncertainty when branching about which variables to f i x at positive integer values in order to obtain quickly an optimal or near optimal solution. Al l of the production mixed IP codes (MPSX/MIP, Ophelie Mixte, UMPIRE) use penalty or pseudo-cost methods to order the variables and preference is given when branching to variables with low penalties. The penalty methods used by these codes involve some heurist ic combination of l inear programming shadow prices and some measure of the extent to which each variable eliminates fractions in the l inear programming solution when the variable is fixed at a positive level. For more det a i l s , the reader is referred to the art icles by Benichou et al. [2], Roy et al. [14], Tomlin [16], or the survey ar t ic le by Geoffrion and Marsten [7]. We present here an exact decomposition method for computing penalties which makes i t possible for most of the columns of a given IP problem to be kept in secondary storage and evaluated in core one at a time. Carried to the extreme our procedure w i l l , without a branch and bound search, reduce the original set of act iv i t ies to a set of optimal act i v i t i e s for the IP problem, and indicate their o p timal non-negative integer levels. I t would appean however, that the method would best be combined with some branch and bound algorithm. The decomposition method begins with a reformulation of the IP problem using group theory and a related IP dual problem from [5] for exploit ing this reformulation. Any optimal solution to the IP dual problem produces a strong Gomory cut, and this cut permits the creation of a stronger IP dual problem. Finite convergence is assured because the cutting plane method converges f i n i t e l y (see Chapter 26 in Dantzig [3]) . During the computation of an optimal solution to each IP dual problem, the IP columns are part i tioned into classes. Each dual solution is used to reorder the elements in a class according to newly computed dual costs. The minimal cost of each class is used in the construction of a shortest route tree. This shortest route tree provides lower bounds for each class that allows us to delete al l act iv i t ies in that class above a certain value of dual cost. I t is important to emphasize that the decomposition method being proposed here uses computational procedures which have proven to be ef f ic ient to compute and effective in solving a variety of real l i f e IP problems (see references [9], [ lO], [ l l ] ) . The method is presented for pure IP problems, but i t can be extended to mixed IP problems by combining the IP duality theory of [5] with Benders' method for mixed IP (see reference [ 1 ] ) . The'problem we wish to study is: Find z* where

Analysis and Synthesis of Sorting Algorithms

Abstract: The problem of analyzing and synthesizing sorting algorithms is studied. That is, given a sorting algorithm we want to investigate how it works in a step-by-step manner and consequently to assert that it indeed arranges the objects according to a certain ordering relationship, and conversely, given an ordering relationship according to which a set of objects are to be arranged, we want to determine an algorithm that will yield the desired result.

Design features of a real-time check-clearing system

Abstract: Banking operations often require complex facilities for their data processing. This application required a multiprocessor configuration controlled by a single job step running continuously for many hours a day. Discussed are the special access methods and recovery procedures designed for this environment. The paper also describes a particularly efficient sorting technique evolved for handling large volumes of paper documents.

Dragee sorting apparatus

Abstract: Apparatus for sorting dragees according to diameter and thickness of the dragees, which apparatus comprises, in combination, (a) plate-type sorting means comprising a perforated surface adjustable in tilt and oscillatable and disposed to receive the dragees to be sorted and, disposed therebelow, (b) roller-type sorting means comprising a plurality of substantially parallel rollers wherein adjacent rollers rotate in opposite directions and wherein the spacing between said rollers is steplessly adjustable.

Some design considerations for a document sorting machine

Abstract: A document reader-sorter is analytically studied to determine the effect of document velocity on the number of documents that can be sorted reliably in a given interval of time, and a formula is derived that relates the effect of various design parameters to the throughput of a document sorting machine. One of these parameters, selector response time (i.e., indexing time), is investigated in detail. Both analytical and graphical design techniques are developed to minimize the response time of the selector. These techniques, which are explained by simple examples, are quite general and can therefore be applied to many other incrementing devices.