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Showing papers on "Sorting published in 1975"


Journal ArticleDOI
N.R. Malik1
01 Oct 1975
TL;DR: Graph Theory and Its Applications to Problems of Society and its Applications to Algorithms and Computer Science.
Abstract: Introductory Graph Theory with ApplicationsGraph Theory with ApplicationsResearch Topics in Graph Theory and Its ApplicationsChemical Graph TheoryMathematical Foundations and Applications of Graph EntropyGraph Theory with Applications to Engineering and Computer ScienceGraphs Theory and ApplicationsQuantitative Graph TheoryApplied Graph TheoryChemical Graph TheoryA First Course in Graph TheoryGraph TheoryGraph Theory with ApplicationsGraph Theory with ApplicationsSpectra of GraphsFuzzy Graph Theory with Applications to Human TraffickingApplications of Graph TheoryChemical Applications of Graph TheoryRecent Advancements in Graph TheoryA Textbook of Graph TheoryGraph Theory and Its Engineering ApplicationsGraph Theory, Combinatorics, and ApplicationsAdvanced Graph Theory and CombinatoricsTopics in Intersection Graph TheoryGraph Theory with Applications to Engineering and Computer ScienceGraph Theory and Its Applications, Second EditionHandbook of Research on Advanced Applications of Graph Theory in Modern SocietyGraph Theory with Applications to Algorithms and Computer ScienceGraph TheoryGraph Theory with Algorithms and its ApplicationsGraph TheoryGraph Theory with ApplicationsGraph Theory ApplicationsHandbook of Graph TheoryGraph Theory and Its Applications to Problems of SocietyBasic Graph Theory with ApplicationsTen

809 citations


Journal ArticleDOI
TL;DR: The worst-case time complexity of algorithms for multiprocessor computers with binary comparisons as the basic operations is investigated and the algorithm for finding the maximum is shown to be optimal for all values of k and n.
Abstract: The worst-case time complexity of algorithms for multiprocessor computers with binary comparisons as the basic operations is investigated. It is shown that for the problems of finding the maximum, sorting, and merging a pair of sorted lists, if n, the size of the input set, is not less than k, the number of processors, speedups of at least $O(k/\log \log k)$ can be achieved with respect to comparison operations. The algorithm for finding the maximum is shown to be optimal for all values of k and n.

412 citations


Journal ArticleDOI
TL;DR: A network which sorts n numbers when used to sort numbers of only two sizes, 0 and 1, can be regarded as forming the n frontal (unate) symmetric boolean functions of n arguments.
Abstract: : A network which sorts n numbers when used to sort numbers of only two sizes, 0 and 1, can be regarded as forming the n frontal (unate) symmetric boolean functions of n arguments. When sorting networks are constructed from comparator modules they appear to require: (1) delay time or number of levels of order (log of n to the base 2) squared, (2) size or number of elements of order (log of n to the base 2) squared, and (3) formula length or number of literals of order n (log of n to the base 2). If one permits the use of negations in constructing the corresponding boolean functions, these three measures of complexity can be reduced to the orders of log of n to the base 2, n, and n to the 5th power respectively. The latter network however is incapable of sorting numbers and may be thought of as merely counting the number of inputs which are 1. One may incorporate this network, however, in a larger network which does sort and in time proportional to only log of n to the base 2. (Author)

177 citations


Patent
14 Jul 1975
TL;DR: In this article, a self service postal apparatus and method printing postage useable for sorting packages and other postal articles is described, and a display of the geographic location of the addressee assures the user that the zip code number is accurate.
Abstract: There is disclosed a self service postal apparatus and method printing postage useable for sorting packages and other postal articles. On entering or dialing the zip code of the addressee a display of the geographic location thereof assures the user that the zip code number is accurate and it may, if desired, activate a computer to compute the postage due. After the customer pays the computed postage, the postage with the zip code of addressee therewith may be printed on the package or label in machine readable form useable for automatic mail sorting.

91 citations


Proceedings ArticleDOI
05 May 1975
TL;DR: It is shown that X + Y can be sorted with O(N2) comparisons and this search method translates into an insertion sort, where the insertions are not performed by means of the usual binary search, but rather as off-centered searches designed so that each comparison equally divides the space of remaining possibilities.
Abstract: Let X = {x1,...,xN} and Y = {y1,...,yN} be sets of N real numbers. We denote by X + Y the multiset {xi + yj; 1 ≤ i, j ≤ N} of size N2. Berklekamp has posed the problem of sorting X + Y. Harper, Payne, Savage and Strauss [1] show that N21og2N comparisons suffice to sort X + Y, thereby saving a factor of 2 over sorting without exploiting the structure of X + Y. (Given u in X + Y, we assume that we know the i,j indices such that u = xi + yj.) Furthermore, they show that this bound is tight for a restricted class of comparison algorithms. However, without their restriction the order of magnitude comparison complexity of this problem has remained an open question. In this paper we show that X + Y can be sorted with O(N2) comparisons. Our proof is unusual for this type of problem in that we do not explicitly exhibit an algorithm. Instead, it is a particular application of a more general search technique whose behavior is easily related to information theoretic lower bounds. In the context of sorting, this search method translates into an insertion sort, where the insertions are not performed by means of the usual binary search, but rather as off-centered searches designed so that each comparison, roughly speaking, equally divides the space of remaining possibilities. We draw attention to this search technique because it might find application to other problems, and we illustrate this possibility with a second application. Our second application concerns the construction of probabilistically balanced binary search trees.

75 citations


Journal ArticleDOI
TL;DR: This paper develops algorithms that are aimed specifically at the hardest possible examples of branch-and-bound algorithms, faster by factors far in excess of 1,000 in many cases, thereby extending considerably the range of practically solvable 0-1 knapsack problems.
Abstract: Branch-and-bound algorithms are adequate for the solution of a wide range of 0-1 knapsack problems. It is shown that the simplest method of branching is as good as any. However, problems with highly correlated large weights and values quickly become unsolvable in a reasonable time. This paper develops algorithms that are aimed specifically at the hardest possible examples. The new methods use merging and sorting ideas and require a moderate amount of additional memory space. They are, however, faster by factors far in excess of 1,000 in many cases, thereby extending considerably the range of practically solvable 0-1 knapsack problems.

48 citations


Journal ArticleDOI
TL;DR: A sorting task which has wide applications in anthropology is discussed, illustrated with a study of English role terms, where several interesting dimensions emerge through multidimensional and hierarchical analyses of the sorting data.
Abstract: This article discusses a sorting task which has wide applications in anthropology. The task is illustrated with a study of English role terms. Several interesting dimensions emerge through multidimensional and hierarchical analyses of the sorting data.

40 citations


Journal ArticleDOI
TL;DR: The application of well- known results to a new problem to save computation time in sorting sets of numbers of the form X q- Y, and the main appeal of the new results, aside from their practical uses, is the diversity of the old ideas behind them.
Abstract: This paper consists of the application of well- known results to a new problem. The problem, posed by E. Berlekamp, was to save computation time in sorting sets of numbers of the form X q- Y. The main appeal of the new results, aside from their practical uses, is the diversity of the old ideas behind them. It is also interesting to see how the modeling of data and computing affect the results: when the model is of sorting n-tupules of real numbers with binary compari- sons, the best result we can do is nalogan comparisons, which is shown to be sharp under certain circumstances; when the model is of sorting n-tuples of integers in the range 0 to n -- 1, on a random-access stored program computer, the time complexity is shown to be on the order of n(logan).

38 citations


Journal ArticleDOI
TL;DR: All three dissimilarity measures for the unconstrained sorting task are metrics, but they differ in the kind of compensation which they make for differences in the sizes of cells within sortings.
Abstract: In this article, three dissimilarity measures for the unconstrained sorting task are investigated. All three measures are metrics, but they differ in the kind of compensation which they make for differences in the sizes of cells within sortings. Empirical tests of the three measures are done with sorting data for occupations names and the names of behaviors, using the multidimensional scaling method.

28 citations


Journal ArticleDOI
TL;DR: Given a one-dimensional set of N points, it is easy, using a sort operation, to find which of them is the nearest neighbor of each point, and it is still possible to salvage some of the attractive properties found in one dimension, provided that the authors are looking for points sufftciently near the given one.

27 citations


Journal ArticleDOI
TL;DR: In this paper, a planning methodology based on Monte Carlo sampling of plans and sorting out inefficient plans according to the rules of stochastic dominance is developed for farm planning under risk, and an application in income stabilization research is indicated.
Abstract: A planning methodology is developed based on Monte Carlo sampling of plans and sorting out inefficient plans according to the rules of stochastic dominance. Illustrations and methodological comparison are made in a context of farm planning under risk, and an application in income stabilization research is indicated.

Journal ArticleDOI
TL;DR: It was concluded that the sorting technique diminished differences in organizational behavior usually found between older and younger subjects.
Abstract: Second graders, fifth graders, and adults participated in 2 experiments designed to study the effects of sorting on subsequent recall of unrelated words. 1 group sorted the items freely, while a second group was constrained to learn the sorting schemes generated by free subjects. In the first experiment, subjects sorted until they reached a criterion of organizational stability. In Experiment 2, sorting was terminated prior to reaching a stable criterion. Recall and output clustering were reduced in Experiment 2, relative to Experiment 1, because of organizational instability. No meaningful differences were found in either experiment in the sorting schemes generated by free subjects in the 3 age groups, nor was there an effect of age of yoking partner on performance of constrained subjects. This result differed from previous research, and it was concluded that the sorting technique diminished differences in organizational behavior usually found between older and younger subjects.

Patent
10 Jun 1975
TL;DR: A sheet sorting machine has a double set of sheet receiving trays and deflector fingers for selectively deflecting successive sheets into alternate trays in the set as mentioned in this paper, which can be used to selectively switch between different trays.
Abstract: A sheet sorting machine has a double set of sheet receiving trays and deflector fingers for selectively deflecting successive sheets into alternate trays in the set.



Patent
22 Jan 1975
TL;DR: A sorting machine consisting of a vertically inclined feed bed, a feeder for feeding objects to an upper portion of the feed bed and a sorting arrangement which is arranged to receive the objects from the said lower portion and to separate them into groups of desired and undesired objects respectively is described in this article.
Abstract: A sorting machine comprising a vertically inclined feed bed, a feeder for feeding objects to be sorted to an upper portion of said feed bed, the feed bed being adapted to be supplied with a fluid which fluidizes the objects thereon so that the latter flow to a lower portion of the feed bed, and a sorting arrangement which is arranged to receive the objects from the said lower portion and to separate them into groups of desired and undesired objects respectively.

Patent
10 Jun 1975
TL;DR: In this paper, an independent machanism was proposed to establish a recognizing function and a sorting function between a normal and false coin respectively by an independent Machanism, which was used to distinguish between real and false coins.
Abstract: PURPOSE: Establishing a recognizing function and a sorting function between a normal and false coins respectively by an independent machanism. COPYRIGHT: (C)1976,JPO&Japio

Patent
21 Jan 1975
TL;DR: An improved coin sorting and counting system is described in this paper, where a rotary hopper feeds the coins one at a time to a downwardly inclined track assembly wherein sensing means detect the presence and determine the denomination of the coins as they move there past.
Abstract: An improved coin sorting and counting apparatus is disclosed. A rotary hopper feeds the coins one at a time to a downwardly inclined track assembly wherein sensing means detect the presence and determine the denomination of the coins as they move therepast. A signal is generated which is proportional to the denomination of each coin and then the signals are totaled. The foregoing Abstract is neither intended to define the invention of the Application which, of course, is measured by the claims, nor is it intended to be limiting as to the scope of the invention in any way.

Patent
13 May 1975
TL;DR: In this article, the article collection apparatus includes a slide which accepts articles discharged from a plurality of article sorting machines that are arranged in elevation one above the other, and guides the items discharged from the plurality of sorting machines such that the articles are caused to follow a path that is in a direction essentially opposite to the direction of the sorting machines' transport movement and at an angle of substantially forty degrees to the horizontal.
Abstract: An apparatus for collection of articles at the discharge ends of article sorting machines, particularly a plurality of sorting machines that are arranged one above the other in elevation, and where it is desired to collect articles discharged by the multiple sorting machines at common collection points without causing damage to the articles. The article collection apparatus includes a slide which accepts articles discharged from a plurality of article sorting machines that are arranged in elevation one above the other, and guides the articles discharged from the plurality of sorting machines such that the articles are caused to follow a path that is in a direction essentially opposite to the direction of the sorting machines' transport movement and at an angle of substantially forty degrees to the horizontal, thereby causing the initial velocity imparted to the articles by the discharge action of the sorting machines to be reduced to zero, and also thereby permitting articles discharged from the plurality of sorting machines arranged one above the other to enter a common slide. The end terminus of the slide is shaped to discharge the articles horizontally into a free fall trajectory. A flexible barrier located in the path of the article trajectory causes the velocity of the articles to be reduced to zero. Beneath the flexible barrier there is a collection receptacle that receives the articles which drop after impacting the flexible barrier. The collection container may have a door located at the bottom that, when opened, permits the articles to drop onto a conveyance means for transporting the articles away from the sorting machines.

Patent
24 Jul 1975
TL;DR: In this paper, an automatic laundry sorting machine comprising separate sorting stations having individually driven conveyor units for feeding and sorting folded laundry articles according to size is described. But it does not specify the size of the items to be released.
Abstract: An automatic laundry sorting machine comprising separate sorting stations having individually driven conveyor units for feeding and sorting folded laundry articles according to size. Sorting and sensing means are associated with at least one of the conveyor units to actuate a release mechanism for articles of selected predetermined size. Articles of other sizes are not released but are passed to subsequent stations where further sorting may occur. Articles not fitting any of the predetermined size-sensing criteria can be passed or by-passed through the conveyor units and discharged outside the system. Alternative embodiments including counters strategically placed in subsequent stations and unique jam eliminating circuitry are described.




Proceedings ArticleDOI
13 Oct 1975
TL;DR: It is proved that an algorithm for selecting both the minimum and maximum element from an unordered set is minimean optimal, namely degree information of the Hasse digraphs.
Abstract: We prove that an algorithm for selecting both the minimum and maximum element from an unordered set is minimean optimal. This algorithm had already been shown to be minimax optimal. The circumstances in which the same algorithm is optimum for both norms leads to a conjecture relating both norms. The method of proof utilizes a new idea in the theory of sorting optimality, namely degree information of the Hasse digraphs.

Patent
29 May 1975
TL;DR: For the handling of devices which at least partly consist of a ferromagnetic material, at least one switchable electromagnet in a fixed position produces an electromagnetic field which penetrates a first steady magnetic field and is dimensioned and timely switched according to the special handling process to be performed.
Abstract: For the handling, especially sorting, of devices which at least partly consist of a ferromagnetic material, at least one switchable electromagnet in a fixed position produces an electromagnetic field which penetrates a first steady magnetic field and is dimensioned and timely switched according to the special handling process to be performed.

Patent
John A. Nelson1
25 Sep 1975
TL;DR: An improved sorter control system for controlling modular sorting assemblies which receive copy sheets from a duplicating machine and distribute the sheets into bins to form collated sets of document information being reproduced is described in this article.
Abstract: An improved sorter control system for controlling modular sorting assemblies which receive copy sheets from a duplicating machine and distribute the sheets into bins to form collated sets of document information being reproduced The control system uses two states of a cam operated switch in conjunction with two contacts of a relay which changes state as a sheet of paper interrupts a light beam in each of the modular sorter assemblies In this manner both the lead edge and the trail edge of a copy sheet breaking and clearing, respectively, the light beam upon entering a bin are recognized causing an index mechanism which controls the sequence of opening the gates for each of the bins to advance The gate last opened directs copy sheets to the next modular sorting assembly to continue the sorting operation

Patent
01 Apr 1975
TL;DR: In this paper, an automatic sorting apparatus in a pipe working system comprising a pipe loading means having hooks to receive a pipe to be bent, the receiving operation of the hooks serving also as a sorting operation for pipe bending.
Abstract: Automatic sorting apparatus in a pipe working system comprising a pipe loading means having hooks to receive a pipe to be bent, the receiving operation of the hooks serving also as a sorting operation for pipe bending.

Patent
23 Jan 1975
TL;DR: The coin tester has a deflector to separate good and bad coins and several further deflectors in the path of the good coins to guide the latter into various sorting channels.
Abstract: The coin tester has a deflector to separate good and bad coins and several further deflectors in the path of the good coins to guide the latter into various sorting channels. The good/bad deflector is pref. operated by a measuring and evaluating circuit for a shorter time than the sorting deflectors. Pref. after handling a good coin the circuit remains blocked for further coins during operation of the sorting deflectors.