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2. Validating Claims for Algorithms Proposed for Publication
- Author
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Ignizio, James P.
- Published
- 1973
3. APPLIED STATISTICS ALGORITHMS SECTION.
- Subjects
MATHEMATICS ,ALGORITHMS ,PAPER ,COMPUTER programming ,TECHNICAL specifications - Abstract
The article presents information on the publication of a book "Applied Statistics, Algorithms," relevant to statistics, by the Royal Statistical Society in cooperation with the Science Research Council's Working Party on Statistical Computing. A policy statement describing the editorial policy appears in "Applied Statistics," Vol. 1. No. 1 (1968). A support paper describing the expected contents of the external specification and making recommendation for the layout of algorithms and for programming strategy will appear in the following issue.
- Published
- 1968
4. Index Ranges for Matrix Calculi.
- Author
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Bayer, R., Witzgall, C., and Gries, D.
- Subjects
MATHEMATICAL analysis ,ALGORITHMS ,DATA structures ,COMPUTER programming ,ELECTRONIC file management ,ELECTRONIC data processing - Abstract
The paper describes a scheme for symbolic manipulation of index expressions which arise as a by-product of the symbolic manipulation of expressions in the matrix calculi described by the authors in a previous paper. This scheme attempts program optimization by transforming the original algorithm rather than the machine code. The goal is to automatically generate code for handling the tedious address calculations necessitated by complicated data structures. The paper is therefore preoccupied with "indexing by position." The relationship of "indexing by name" and "indexing by position" is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
5. COMMENTS ON A PAPER BY ROMESH SAIGAL: "A CONSTRAINED SHORTEST ROUTE PROBLEM".
- Author
-
Rosseel, Marc
- Subjects
LINEAR programming ,ALGORITHMS ,VECTOR algebra ,COMPUTER programming ,CONSTRAINTS (Physics) ,DYNAMIC programming ,MATRICES (Mathematics) ,DISTANCES - Abstract
The article presents a zero-one linear program and a dynamic programming algorithm for finding the shortest route containing exactly q arcs from node 1 to node n in a network (N, A) with distances c(i, j). This note shows that the linear programming formulation and his extension based on it are defective, and that the dynamic programming algorithm can lead to suboptimal solutions, but a minor change in the dynamic programming formulation relieves the difficulty. A special feature of this linear program is that there can never be a loop in the basis, because the vectors corresponding to the variables of a loop are linearly dependent. The last comment is related to the dynamic programming algorithm. One is allowed to pass through a node more than once in the shortest route . The proposed method for solving this program consists of converting it into a shortest route problem containing exactly q arcs. But for some arbitrary reason, the dynamic program is formulated in such a way that one can never have starting node 1 more than once in the final solution.
- Published
- 1968
- Full Text
- View/download PDF
6. A TIME-SHARING COMPUTER PROGRAM FOR THE SOLUTION OF THE MULTIPLE CRITERIA PROBLEM.
- Author
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Dyer, James S.
- Subjects
MULTIPLE criteria decision making ,TIME-sharing computer systems ,INTERACTIVE computer systems ,HUMAN-machine systems ,DECISION making ,PROBLEM solving research ,COMPUTER software ,COMPUTER programming ,ALGORITHMS - Abstract
This note presents a description of a time-sharing computer program written to implement a man-machine interactive algorithm for the solution of the multiple criteria problem. The interactive algorithm was suggested in a recent paper by Geoffrion, "Vector Maximal Decomposition Programming," Working Paper No. 164, Western Management Science Institute, University of California, Los Angeles, September 1970. A unique feature of this program is the man-machine dialog which obtains information from the decision-maker through a series of simple, ordinal comparisons. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
7. Algorithms.
- Author
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Paciorek, Kathleen A. and Fosdick, L. D.
- Subjects
ALGORITHMS ,COMPUTERS ,ELECTRONIC systems ,FORTRAN ,COMPUTER programming - Abstract
The article presents several research papers relating to algorithms. The paper "Greatest Common Divisor of n Integers and Multipliers" presents an algorithm which calculates the greatest common divisor, IGCD, of n integers. Details of the method and comparisons to other algorithms are also given. The algorithm is a new version of the Euclidean algorithm for n integers. The n-1 calculations of the greatest common divisor of two integers is accomplished by means of a modified version of the Blankinship algorithm. The paper "Exponential Integral Ei (x)" presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration. It presents an algorithm which was compiled and executed without any modification on a UNIVAC 1108 computer. An unfortunate precedent has been set in several recent algorithms of using an illegal FORTRAN construction.
- Published
- 1970
8. Incorporating Origin Shifts into the QR Algorithm for Symmetric Tridiagonal Matrices.
- Author
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Stewart, G. W. and Timlake, W. P.
- Subjects
EIGENVALUES ,ALGORITHMS ,MATRICES (Mathematics) ,COMPUTER programming ,MATHEMATICAL functions ,STOCHASTIC convergence - Abstract
The QR iteration for the eigenvalues of a symmetric tridiagonal matrix can be accelerated by incorporating a sequence of origin shifts. The origin shift may be either subtracted directly from the diagonal elements of the matrix or incorporated by means of an implicit algorithm. Both methods have drawbacks: the direct method can unnecessarily degrade small eigen-values, while the implicit method can effectively loose the shift and thereby retard the convergence. This paper presents a new method which has neither drawback. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
9. An Implemented Graph Algorithm for Winning Shannon Switching Games.
- Author
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Chase, Stephen M.
- Subjects
GRAPH algorithms ,COMPUTER programming ,COMPUTER software ,COMPUTERS ,VIDEO gamers ,ALGORITHMS ,VIDEO games - Abstract
Describes a computer program for the implementation of graph algorithms which wins Shannon Switching Games. Difference in the goals between players of the game; Existence of a winning strategy between players; Effect of ease of communication between players on computer program demonstration.
- Published
- 1972
- Full Text
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10. The Reconstruction of Binary Patterns from Their Projections.
- Author
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Shi-Kuo Chang
- Subjects
BINARY number system ,COMPUTER algorithms ,NUMBER systems ,COMPUTER arithmetic ,COMPUTER programming ,ALGORITHMS - Abstract
Given the horizontal and vertical projections of a finite binary pattern f, can we reconstruct the original pattern f? In this paper we give a characterization of patterns that ore reconstructable from their projections. Three algorithms ore developed to reconstruct both unambiguous and ambiguous patterns, it is shown that an unambiguous pattern can be perfectly reconstructed in time m × n and that a pattern similar to an ambiguous pattern can also be constructed in time m × n, where m, n are the dimensions of the pattern frame. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
11. Analysis of Algorithms for the Zero-One Programming Problem.
- Author
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Gue, Ronald L., Liggett, John C., Cain, Kenneth C., and Emery, J.
- Subjects
COMPUTER programming ,ALGORITHMS ,PROBLEM solving ,ELECTRONIC data processing ,INFORMATION storage & retrieval systems ,MATHEMATICAL analysis - Abstract
This paper is concerned with a review and examination of several existing algorithms for the zero-one programming problem. Computational experience is summarized. The machine time and storage requirements of several of the algorithms are compared over several test problems of small and intermediate size. Computer experiments still provide little hope of solving problems with over 100 variables with a reasonable amount of machine time. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
12. A NOTE ON PARAMETRIC NETWORK FLOWS.
- Author
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Minieka, Edward
- Subjects
ALGORITHMS ,COMPUTER algorithms ,COMPUTER networks ,NETWORK PC (Computer) ,LINEAR programming ,DATA flow computing ,MODULES (Algebra) ,MATHEMATICAL programming ,COMPUTER programming ,SPANNING trees - Abstract
In their paper [1], Doulliez and Rao present algorithms that solve two flow problems for a single source, multi-terminal network. The first problem that they solve is the construction of a flow that maximizes the value of t, where the demand at each sink is a nondecreasing, linear function of t. Given such a flow, the second problem that they solve is the construction of a flow that maximizes the value of t when the capacity of an arc is reduced. This paper supplies a finiteness proof for the first algorithm and sketches a finiteness proof for the second algorithm. The proofs are based on the well-known fact that a network possesses only a finite number of different spanning trees. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
13. A SEQUENTIAL ALGORITHM FOR A CLASS OF PROGRAMMING PROBLEMS WITH NONLINEAR CONSTRAINTS.
- Author
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Jagannathan, R.
- Subjects
THEORY of constraints ,SEQUENTIAL analysis ,NONLINEAR programming ,MANAGEMENT science ,ALGORITHMS ,CONJUGATE gradient methods ,QUADRATIC programming ,COMPUTER programming ,ECONOMIC convergence - Abstract
The purpose of this paper is to furnish a computational scheme for a class of programming problems with nonlinear constraints. The algorithm is sequential in nature, producing a sequence of feasible solutions whose limit points are optimal solutions of the original problem. Further, with a view to accelerating convergence we suggest two variants of the solution procedure. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
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14. PUBLIC FACILITIES LOCATION UNDER STOCHASTIC DEMAND.
- Author
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Carbone, Robert
- Subjects
PUBLIC utilities ,ROADS ,STOCHASTIC analysis ,MATHEMATICAL analysis ,STOCHASTIC processes ,MATHEMATICAL programming ,ALGORITHMS ,COMPUTER programming ,FUNCTIONAL equations - Abstract
This paper extends the current state of public facilities location problems on a road network to cover situations in which the number of users at each node may be a random variable. The basic location model is reformulated as a chance-constrained programming problem with fractile criterion. A computational procedure for solving the non-linear deterministic equivalent problem derived is presented. Finally, a hypothetical numerical example illustrates the possibility of changes in the location decision when the stochastic nature of the problem is taken into account. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
15. PARAMETRIC PROGRAMMING AND THE PRIMAL-DUAL ALGORITHM.
- Author
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Kelley Jr., J. E.
- Subjects
ALGORITHMS ,MATHEMATICAL programming ,OPERATIONS research ,COMPUTER programming ,FUNCTIONAL equations ,MATHEMATICAL optimization - Abstract
This paper studies the close relation between the Gass-Saaty parametric programming algorithm and the `primal-dual' procedures recently exploited by DANTZIG, FORD, AND FULKERSON lit is shown that the two procedures are equivalent The possibility of eliminating the two-phase character of the simplex method using these techniques is discussed Finally, the application of the techniques to problems with special structure is considered [ABSTRACT FROM AUTHOR]
- Published
- 1959
- Full Text
- View/download PDF
16. ELEMENTS OF LARGE-SCALE MATHEMATICAL PROGRAMMING PART I: CONCEPTS.
- Author
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Geoffrion, Arthur M.
- Subjects
MATHEMATICAL programming ,MANAGEMENT science ,ALGORITHMS ,COMPUTER programming ,MATHEMATICAL optimization ,OPERATIONS research ,LINEAR programming ,LARGE scale systems ,BUSINESS mathematics ,MATHEMATICAL analysis ,MATHEMATICAL models - Abstract
A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming. These concepts fall into two categories. The first category consists of problem manipulations that can be used to derive what are often referred to as "master" problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization. The second category consists of solution strategies that can be used to solve the master problems, often with the result that "subproblems" arise which can then be solved by specialized algorithms. The Piecewise, Restriction, and Relaxation strategies are the principal ones discussed. Numerous algorithms found in the literature are classified according to the manipulation/strategy pattern they can be viewed as using, and the usefulness of the framework is demonstrated by using it (see Part II of this paper) to rederive a representative selection of algorithms. The material presented is listed in the following order: The first section is introductory in nature, and discusses types of large-scale problems, the scope of discussion and the literature, and the notation used. The second section, entitled "Problem Manipulation: Source of 'Master' Problems" covers the subjects of projection, inner linearization and outer linearization. The third section, "Solution Strategies: Source of 'Subproblems'," discusses piecewise strategy, restriction and relaxation. The fourth section is entitled "Synthesizing Known Algorithms from Manipulations and Strategies," and is followed by a concluding section and an extensive bibliography. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
17. DUALITY IN DISCRETE PROGRAMMING: II. THE QUADRATIC CASE.
- Author
-
Balas, Egon
- Subjects
QUADRATIC equations ,QUADRATIC programming ,MATHEMATICAL programming ,COMPUTER programming ,FUNCTIONAL equations ,ALGORITHMS ,NONLINEAR programming ,DYNAMIC programming ,INTEGER programming ,CONSTRAINT satisfaction ,MATHEMATICAL variables - Abstract
This paper extends the results of "Duality in Discrete Programming" [1] to the case of quadratic objective functions. The paper is, however, self-contained. A pair of symmetric dual quadratic programs is generalized by constraining some of the variables to belong to arbitrary sets of real numbers. Quadratic all-integer and mixed-integer programs are special cases of these problems. The resulting primal problem is shown, subject to a qualification, to have an optimal solution if and only if the dual has one, and in this case the values of their respective objective functions are equal. The dual of a mixed-integer quadratic program can be formulated as a minimax problem whose quadratic objective function is linear in the integer-constrained variables, and whose linear constraint set does not contain the latter. Based on this approach an algorithm is developed for solving integer and mixed-integer quadratic programs. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
18. Minimax Logarithmic Error.
- Author
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Dunham, Charles B.
- Subjects
COMPUTER algorithms ,LOGARITHMIC functions ,SQUARE root ,LOGARITHMS ,ALGORITHMS ,COMPUTER programming ,COMPUTER arithmetic - Abstract
The article discusses the computation of rational approximations using existing algorithms. In a recent paper it is shown that minimax logarithmic approximations are optimal for square root calculations, making the minimax logarithmic problem of practical interest. The authors point out how rational approximations which are best with respect to maximum logarithmic error can be computed by existing algorithms. Suppose one wishes to approximate a positive continuous function "f" by a positive rational function R, then the logarithmic error at a point x is log (f(x))-- log (R(x)). The approximation problem is thus equivalent to ordinary approximation of continuous function g = log (f) by log {R).
- Published
- 1969
- Full Text
- View/download PDF
19. An Alogorithm for Generating Structural Surrogates of English Text.
- Author
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Strong, Suzanne M.
- Subjects
COMPUTER algorithms ,ALGORITHMS ,SYNTAX (Grammar) ,GRAMMAR ,COMPUTER programming ,VOCABULARY - Abstract
This paper describes the development and application of an algorithm which generates non-linear representations of English text. The algorithm uses the results of a syntactic analysis system and a set of rules which prescribe linkages to generate a graph of a sentence. The shape of these graphs corresponds to the syntax of the sentence; the labels correspond to the vocabulary of the sentence and the edge types correspond to case grammar roles. The sentence graphs can then be interconnected at common nodes and analyzed according to common edges. Preliminary experimentation has yielded promising results. It appears that the algorithm produces a representation of English text which could be quite useful in automatic language processing. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
20. AUGMENTED THREADED INDEX METHOD FOR NETWORK OPTIMIZATION.
- Author
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Glover, F., Klingman, D., and Stutz, J.
- Subjects
ALGORITHMS ,COMPUTER networks ,COMPUTER algorithms ,COMPUTER programming ,COMPUTER storage devices ,COMPUTER input-output equipment ,ELECTRONIC data processing ,INFORMATION networks ,DATA transmission systems - Abstract
Easily manipulated list structures for recording the basis tree for adjacent extreme point (“simplex type”) network algorithms are paramount to the development of computationally efficient network algorithms. This paper presents a new list structure which is shown to be computationally more efficient and to require one-third less computer memory to implement than all alternate list structures. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
21. Extensions of the Evans-Gould Stability Theorems for Mathematical Programs.
- Author
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Greenberg, Harvey J. and Pierskalla, William P.
- Subjects
MATHEMATICAL programming ,ALGORITHMS ,COMPUTER programming ,PERTURBATION theory ,APPROXIMATION theory ,FUNCTIONAL analysis - Abstract
This paper extends the results of Evans and Gould for stability in mathematical programming. In particular, it shows that their conditions apply to functional perturbation, to equality constraints, and to policy stability under certain conditions. Further, it shows that strictly monotonic programs and positively homogeneous programs possess the closure property needed for stability. Finally, some necessary and sufficient conditions are presented for lower and upper semicontinuity of certain point-to-set mappings. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
22. AN INVERSE-BASIS METHOD FOR BEALE'S QUADRATIC PROGRAMMING ALGORITHM.
- Author
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Land, A. H. and Morton, G.
- Subjects
QUADRATIC programming ,COMPUTER algorithms ,NONLINEAR programming ,MATHEMATICAL programming ,DYNAMIC programming ,ALGORITHMS ,INVERSE functions ,COMPUTER programming - Abstract
This paper presents a version of Beale's Quadratic Programming Algorithm [1], [2] for solving a problem of maximizing a quadratic function under linear constraints. The modification discussed here makes it possible to retain the "inverse basis" tableau which has to be augmented by additional constraints to be called "auxiliary." The algorithm has been successfully tested on a computer. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
23. A BRANCH SEARCH ALGORITHM FOR THE KNAPSACK PROBLEM.
- Author
-
Greenberg, Harold and Hegerich, Robert L.
- Subjects
KNAPSACK problems ,INTEGER programming ,MATHEMATICAL programming ,BRANCH & bound algorithms ,ALGORITHMS ,NETWORK analysis (Planning) ,MATHEMATICAL optimization ,COMPUTER programming ,MATHEMATICAL models ,MATHEMATICAL analysis ,OPERATIONS research ,PROBLEM solving - Abstract
This paper presents an algorithm for the solution of the knapsack problem. The method involves searching the nodes of a tree along a single branch at a time. The algorithm eliminates the computational drawbacks inherent in the usual branch and bound schemes. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
24. PLANT LOCATION WITH GENERALIZED SEARCH ORIGIN.
- Author
-
Spielberg, Kurt
- Subjects
INDUSTRIAL location ,SEARCH engine programming ,COMPUTER programming ,MATHEMATICAL optimization ,FACILITY management ,FACTORY management ,LOCATION analysis ,ALGORITHMS ,INDUSTRIAL management ,DECISION making ,OPERATIONS research - Abstract
There exists computational experience to the effect that search algorithms of the type introduced by Balas are frequently ineffective because of being tied to a rigid "natural" search origin. In this paper the dynamic relocation of the search origin to possibly more appropriate points is advocated. Details of such a procedure are given for the Simple Plant Location Problem. Computational improvements of, sometimes, a striking nature are presented. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
25. AN ALGORITHM FOR SEPARABLE NONCONVEX PROGRAMMING PROBLEMS.
- Author
-
Falk, James E. and Soland, Richard M.
- Subjects
ALGORITHMS ,NONCONVEX programming ,COMPUTATIONAL complexity ,FOUNDATIONS of arithmetic ,MATHEMATICAL models in business ,MATHEMATICAL programming ,MANAGEMENT science ,BRANCH & bound algorithms ,INTEGER programming ,COMPUTER programming ,MATHEMATICAL optimization ,BUSINESS mathematics - Abstract
In this paper we present an algorithm for solving mathematical programming problems of the form: Find x = (x[sub 1], ..., x[sub n]) to minimize Σφ[sub i] (x[sub i]) subject to x ε G and I ≤ x ≤ L. Each φ[sub i] is assumed to be lower semicontinuous, possibly nonconvex, and G is assumed to be closed. The algorithm is of the branch and bound type and solves a sequence of problems in each of which the objective function is convex. These problems correspond to successive partitions of the feasible set. Two different rules for refining the partitions are considered; these load to convergence of the algorithm under different requirements on the problem functions. Examples are given, and computational considerations are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
26. AN ALGORITHM FOR THE CHEBYSHEV PROBLEM--WITH AN APPLICATION TO CONCAVE PROGRAMMING.
- Author
-
Zangwill, Willard I.
- Subjects
ALGORITHMS ,MATHEMATICAL programming ,CHEBYSHEV series ,CHEBYSHEV systems ,CHEBYSHEV approximation ,COMPUTER programming ,COMPUTER algorithms ,CONVEX programming ,CONCAVE functions ,EDUCATION - Abstract
The Chebyshev problem is to determine a point χ
α which solves maxα min i = 1, ···, N{gi (χ)}. By exploiting generalized inverses an algorithm is developed for determining χα . It is also shown that in a certain sense the Chebyshev problem is equivalent to the concave programming problem. Moreover, for the programming problem generated by the Chebyshev problem, the Kuhn-Tucker conditions are proven to be sufficient even though the feasible region may not be convex. [ABSTRACT FROM AUTHOR]- Published
- 1967
- Full Text
- View/download PDF
27. THE EXTENSION OF THE CASCADE ALGORITHM TO LARGE GRAPHS.
- Author
-
Land, A. H. and Stairs, S. W.
- Subjects
FOUNDATIONS of arithmetic ,COMPUTER programming ,BRANCH & bound algorithms ,COMPUTER algorithms ,MATRICES (Mathematics) ,ALGORITHMS ,GRAPHIC methods ,GROUP extensions (Mathematics) ,MATHEMATICAL models ,EDUCATION - Abstract
Large graphs for which the calculation of the shortest distances between all vertices is required often consist of several parts with limited interconnections. This paper shows how this characteristic may be used to reduce computer storage for a matrix type calculation, to reduce calculational labour, and to provide results in a form which is particularly convenient if a subsequent assignment of commodity flow to shortest paths is needed. The technique presented here allows the partition to be arbitrary, save for a single, easily achieved, condition. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
28. MATRIX ROUNDING PROBLEMS.
- Author
-
Bacharach, Michael
- Subjects
MATRICES (Mathematics) ,ABSTRACT algebra ,CATALECTICANT matrices ,COMPUTER programming ,MATHEMATICAL analysis ,ALGORITHMS ,EXISTENCE theorems ,MATHEMATICAL models ,NETWORK analysis (Planning) ,EDUCATION - Abstract
The problem considered in this paper is that of consistently rounding off the elements of a matrix and its row and column sums. It is shown that a class of rounding problems of this kind is equivalent to a class of problems of determining flows through networks having arbitrary lower as well as upper bounds on edge flows. An existence theorem first proved by Hoffman for flows in such networks is used to show that an important subclass of the matrix rounding problems considered is always soluble. An algorithm for the entire class is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
29. CONSTRUCTION OF SCHOOL TIMETABLES BY FLOW METHODS.
- Author
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de Werra, D.
- Subjects
HEURISTIC ,ALGORITHMS ,SCHOOLS ,TIME ,COMPUTER programming ,HEURISTIC programming - Abstract
Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 1971
- Full Text
- View/download PDF
30. Conversion of Limited- Entry Decision Tables to Computer Programs--A Proposed Modification to Pollack's Algorithm.
- Author
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Shwayder, Keith and Morris, R.
- Subjects
ENTROPY (Information theory) ,INFORMATION theory ,COMPUTER programming ,ALGORITHMS ,COMPUTER software - Abstract
Pollack has proposed on algorithm for converting decision tables into flowcharts which minimize subsequent execution time when compiled into a computer program. Two modifications a this algorithm are proposed. The first relies on Shannon's noiseless coding theorem and the communications concept of entropy but does not completely test the ELSE Rule. The second modification completely tests the ELSE Rule but results in more executions than the first modification. Both modifications result in lower execution time than Pollack's algorithm. However, neither modification guarantees a globally optimal solution. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
31. An Algorithm for Filon Quadrature.
- Author
-
Chase, Stephen M. and Fosdick, Lloyd D.
- Subjects
ALGORITHMS ,NUMERICAL analysis software ,NUMERICAL integration ,NUMERICAL analysis ,MATHEMATICAL analysis ,COMPUTER programming - Abstract
An algorithm for Filon quadrature is described. Considerable attention has been devoted to an analysis of the round-off and truncation errors. The algorithm includes an automatic error control feature. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
32. Additional Results on Key-to-Address Transform Techniques: A Fundamental Performance Study on Large Existing Formatted Files.
- Author
-
Lurn, V. Y. and Yuen, P. S. T.
- Subjects
ELECTRONIC file management ,DATABASE management ,ALGORITHMS ,INFORMATION storage & retrieval systems ,ELECTRONIC data processing ,FORMATTING of information display systems ,COMPUTER programming - Abstract
The article focuses on key-to-address transformation techniques and the results of a performance study on large existing formatted files. The experimental results comparing six commonly used key-to-address transformation techniques were presented by the researchers. One transformation in the study referred to as "generalized radix transformation method" is an elaborate technique based on radix transformation. This method of transformation consists of a radix transformation algorithm as well as hardware implementation to carry out the steps of this transformation in an efficient manner. The intricacy of the generalized radix transformation method has motivated researchers to conduct further studies of the technique. The additional results are presented after a brief description of the basic algorithm used in this generalized radix transformation method. Additional experiments on the files showed that the distribution of the keys was particularly sensitive to the arbitrary selection of an 8-bit grouping.
- Published
- 1972
33. Additional Results on Key-to-Address Transform Techniques: A Fundamental Performance Study on Large Existing Formatted Files.
- Author
-
Lum, V. Y. and Yuen, P. S. T.
- Subjects
ELECTRONIC file management ,FORMATTING of information display systems ,DATABASE management ,INFORMATION storage & retrieval systems ,ALGORITHMS ,ELECTRONIC data processing ,COMPUTER programming - Abstract
The article provides an analysis of key-to-address transformation techniques and the results of a performance study on large existing formatted files. The experimental results comparing six commonly used key-to-address transformation techniques were presented by the researchers. One transformation in the study referred to as "generalized radix transformation method" is an elaborate technique based on radix transformation. This method of transformation consists of a radix transformation algorithm as well as hardware implementation to carry out the steps of this transformation in an efficient manner. The intricacy of the generalized radix transformation method has motivated researchers to conduct further studies of the technique. The additional results are presented after a brief description of the basic algorithm used in this generalized radix transformation method. Additional experiments on the files showed that the distribution of the keys was particularly sensitive to the arbitrary selection of an 8-bit grouping.
- Published
- 1972
- Full Text
- View/download PDF
34. Short Communications.
- Author
-
sattley, Kirk and Millstein, Robert
- Subjects
COMPUTER programming ,ALGORITHMS ,COMPUTER operating systems ,INFORMATION retrieval ,MATHEMATICAL models ,ELECTRONIC data processing ,PROGRAMMING languages - Abstract
Comments on articles published in earlier issues of the journal "Communications of the ACM." Discussion on techniques used in automatic segmentation of cyclic program structures;Focus on diverse techniques to assure the integrity of a data base;Information on algorithms to be followed by primitives in order to maximize the amount of parallel activity in a data base.
- Published
- 1970
35. Concurrent Programming Concepts.
- Author
-
Hansen, Per Brinch
- Subjects
- *
MULTIPROGRAMMING (Electronic computers) , *COMPUTER monitors , *COMPUTER terminals , *COMPUTER programming , *ALGORITHMS , *COMPUTERS - Abstract
This paper describes the evolution of language features for multiprogramming from event queues and semaphores to critical regions and monitors. It suggests that the choice of language concepts should be guided by two simple principles: First, it should be possible to understand a concurrent program in time- independent terms by an effort proportional to its size; secondly, it should be possible to state assumptions about invariant relationships among program components and have these assumptions checked automatically. The central problems of multiprogramming are illustrated by annotated algorithms written in a well-structured programming language. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
36. On an Algorithm of Ghare and Taylor.
- Author
-
McLeavey, Dennis W.
- Subjects
COMPUTER algorithms ,COMPUTER programming ,ALGORITHMS ,ALGEBRA ,MATHEMATICS ,OPERATIONS research - Abstract
This note points out an example in which an algorithm reported by P. M. GHASS AND R. E. TAYLOR [Opns. Res. 17, 838–847 (1969)] for determining optimum redundancy in a series system does not produce an optimal solution. It presents the Ghare-Taylor solution along with a better feasible solution, and explains the necessary corrections to the Ghare-Taylor algorithm and the cause of the difficulty with it. The note thus questions the validity of the computer times reported by Ghare and Taylor and indicates a source yielding computer times for the corrected algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
37. Sorting.
- Author
-
Martin, William A.
- Subjects
- *
SORTING (Electronic computers) , *COMPUTER algorithms , *COMPUTER programming , *ELECTRONIC data processing , *ALGORITHMS - Abstract
The bibliography appearing at the end of this article lists 37 sorting algorithms and 100 books and papers on sorting published in the last 20 years. The basic ideas presented here have been abstracted from this body of work, and the best algorithms known are given as examples. As the algorithms are explained, references to related algorithms and mathematical or experimental analyses are given. Suggestions are then made for choosing the algorithm best suited to a given situation. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
38. Letters to the Editor.
- Author
-
Durstine, Richard M. and Davis, Russell G.
- Subjects
LETTERS to the editor ,MATHEMATICAL programming ,MATHEMATICAL statistics ,ALGORITHMS ,COMPUTER programming ,DEVELOPING countries - Abstract
Presents several letters to the editor related to mathematical programming. Comments on the educational planning in developing nations; Focuses on zero-one programming problems; Information on the criterion equivalence in discrete dynamic programming; Comments on the nuclear bomb causalities from two different urban models.
- Published
- 1969
- Full Text
- View/download PDF
39. APPLICATION OF COMBINATIONAL PROGRAMMING TO A CLASS OF ALL-ZERO-ONE INTEGER PROGRAMMING PROBLEMS.
- Author
-
Pierce, John F.
- Subjects
COMBINATORICS ,INTEGER programming ,PROBLEM solving ,FEASIBILITY studies ,MATHEMATICAL programming ,BINARY number system ,COMPUTER programming ,COMBINATORIAL optimization ,MATHEMATICAL optimization ,KNAPSACK problems ,ALGORITHMS ,COMPUTER algorithms ,DYNAMIC programming ,ASSEMBLY line balancing - Abstract
Problem-solving procedures based on the methods of combinatorial programming are presented for solving a class of integer programming problems in which all elements are zero or one. All of the procedures seek first a feasible solution and then successively better and better feasible solutions until ultimately one is discovered which is shown to be optimal. By representing the problem elements in a binary computer as bits in a word and employing logical "and" and "or" operations in the problemsolving process, a number of problems involving several hundred integer variables have been solved in a matter of seconds. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
40. An Ambiguity in the Description of ALGOL 60.
- Author
-
Herriot, John G.
- Subjects
- *
ALGOL (Computer program language) , *PROGRAMMING languages , *ELECTRONIC data processing , *ALGORITHMS , *COMPUTER programming , *COMPUTER software - Abstract
The article focuses on a paper indicating the error of algorithmic language ALGOL 60 pointed up by the Algorithm 355 construct in the October 1969 issue of the periodical "Communications of the Automation for Computing Machinery." The procedure statement "p" occurs in the body of this procedure, showing "p" to be a procedure without parameters. As originally submitted, the algorithm contained several procedure statements in which p was replaced by a procedure statement. It is possible that the authors of ALGOL 60 intended to permit this but they did not do so. The author's original form may have been more in the sprit of the ALGOL 60 report but the published form confirms to the syntax of ALGOL 60 as described in the report.
- Published
- 1969
- Full Text
- View/download PDF
41. Algorithm 446 Ten Subroutines for the Manipulation of Chebyshev Series [C1].
- Author
-
Fosdick, L. D. and Cline, A. K.
- Subjects
CHEBYSHEV series ,ALGORITHMS ,SUBROUTINES (Computer programs) ,COMPUTER software ,COMPUTER programming ,CHEBYSHEV polynomials - Abstract
The article discusses algorithm 446 with regard to ten subroutines for the manipulation of Chebyshev series. The operations performed in the article are the construction of the Chebyshev approximation of functions, the evaluation of the series or their derivative, the integration or differentiation and the construction of negative or fractional powers of such a series. The subroutines are written in ANSI Fortran. They have been used without modification on such computers as the IBM-7094, IBM-360/93 and Univac 1108. The ten subroutines are considered as a single set, principally because they all use the same storage philosophy. All information is transmitted through the CALL-sequence rather than through the use of COMMON statements. Therefore, the user must provide storage for all the series in his main program, taking into account that all operations are performed in double precision. The coefficients of each series occupy a one-dimensional double-precision array according to the rules of ANSI Fortran. When several Chebyshev series are being manipulated, it is convenient to store all the series in a matrix.
- Published
- 1973
42. Optimizing Binary Trees Grown with a Sorting Algorithm.
- Author
-
Benjamin, R., Martin, W. A., and Ness, D. N.
- Subjects
ALGORITHMS ,ALGEBRA ,COMPUTER programming ,FOUNDATIONS of arithmetic ,MATHEMATICAL models - Abstract
Items can be retrieved from binary trees grown with a form of the Algorithm Quicksort in an average time proportional to log n, where n is the number of items in the tree. The binary trees grown by this algorithm sometimes have some branches longer than others; therefore, it is possible to reduce the average retrieval time by restructuring the tree to make the branches as uniform in length as possible. An algorithm to do this is presented. The use of this algorithm is discussed, and it is compared with another which restructures the tree after each new item is added. [ABSTRACT FROM AUTHOR]
- Published
- 1972
43. Toward an Understanding of Data Structures.
- Author
-
Earley, Jay and Gries, D.
- Subjects
DATA structures ,COMPUTER programming ,ALGORITHMS - Abstract
Presents a notation for describing the semantics of data structures. Implementation facility which could be a part of a programming language; Expression of the semantics of an algorithm; Efficiency of the structures.
- Published
- 1971
- Full Text
- View/download PDF
44. Software and Patents: A Status Report.
- Author
-
Galbi, Elmer W.
- Subjects
COMPUTER programming ,ALGORITHMS ,COMPUTER network resources - Abstract
Reports on developments concerning the legal protection of computer programming. Patentability of algorithms; Summary of the vacillation in court and administrative rulings in computer programming; Proposals made for the legislation in the said area.
- Published
- 1971
- Full Text
- View/download PDF
45. On the Probability Distribution of the Values of Binary Trees.
- Author
-
Hurwitz, Jr., H.
- Subjects
COMPUTER programming ,INTEGRAL equations ,ALGORITHMS ,COMPUTER arithmetic ,FUNCTIONAL equations ,FUNCTIONAL analysis - Abstract
An integral equation is derived for the generating function for binary tree values, the values reflecting sorting effort. The analysis does not assume uniformly distributed branching ratios, and therefore is applicable to a family of sorting algorithms discussed by Hoare, Singleton, and van Emden. The solution to the integral equation indicates that using more advanced algorithms in the family makes only minor reductions in the expected sorting effort, but substantially reduces the variance in sorting effort. Statistical tests of the values of several thousand trees containing up to 10,000 points have given first, second, and third moments of the value distribution function in satisfactory agreement with the moments computed from the generating function. The empirical tests, as well as the analytical results, are in agreement with previously published results for the first moment in the cases of uniform and nonuniform distribution of branching ratio, and for the second moment in the case of uniform distribution of branching ratio. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
46. Proof of a Program: FIND.
- Author
-
Hoare, C. A. R. and Gries, D.
- Subjects
COMPUTER algorithms ,COMPUTER software ,COMPUTER files ,ERRORS ,ALGORITHMS ,COMPUTER programming ,PROGRAMMING languages - Abstract
A proof is given of the correctness of the algorithm "Find." First, an informal description is given of the purpose of the program and the method used. A systematic technique is described for constucting the program proof during the process of coding it, in such a way as to prevent the intrusion of logical errors. The proof of termination is treated as a separate exercise. Finally, some conclusions relating to general programming methodology are drawn. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
47. Algorithms.
- Author
-
Smith, Robert R., McCall, Dennis, Dial, Robert B., and Voorhees, Alan M.
- Subjects
ALGORITHMS ,COMPUTER programming ,INTEGER programming ,COULOMB functions ,WAVE functions ,MATHEMATICS - Abstract
This article discusses several algorithms applicable to computer programming. In programs for special series summation, the algorithm requires only integer arithmetic and can be implemented in algebraic languages. Changes in Coulomb wave functions that will not completely eliminate the overflow problems encountered in the generation of intermediate arrays are presented.
- Published
- 1970
- Full Text
- View/download PDF
48. Algorithms.
- Author
-
Fosdick, L. D.
- Subjects
ALGORITHMS ,COMPUTER software ,COMPUTER programming ,PROGRAMMING languages ,INDUSTRIAL efficiency ,COMPUTER printers - Abstract
This article presents information on a procedure that is a part of a large program which produces the card stunts for the Stanford University football game half-times. The initial development was done by L. Breed, L. Tesler, and J. Sauter. The author made many further developments on this program which included producing an algorithm for coloring in polygonal regions. Prior to the development of this algorithm, there were many cases which did not work. The larger program takes as input an English description of the stunts and produces as output an image of each flip, as a rectangle that has 45 rows with 77 seats in each row. The main program, which will be considered the driver program for the purpose of the procedure drawarea, does all of the handling of the definition of regions and also the printing of the images. It should be mentioned that the procedure drawarea in the actual program is just part of a larger procedure and that all of the parameters are global in order to increase efficiency.
- Published
- 1969
49. On the Downhill Method.
- Author
-
Timlake, W. T. and Bach, H.
- Subjects
FORTRAN ,PROGRAMMING languages ,ALGORITHMS ,ALGEBRA ,STOCHASTIC convergence ,COMPUTER programming - Abstract
The downhill method is a numerical method for solving complex equations f(z) = 0 on which the only restriction is that the function w = f(z) must be analytical. An introduction to this method is given and a critical review of relating literature is presented. Although in theory the method always converges, it is shown that a fundamental dilemma exists which may cause o breakdown in practical applications. To avoid this difficulty and to improve the rate of convergence toward a root, some modifications of the original method are proposed and a program (FORTRAN) based on the modified method is given in Algorithm 365. Some numerical examples are included. [ABSTRACT FROM AUTHOR]
- Published
- 1969
50. Generation of Optimal Code for Expressions via Factorization.
- Author
-
McClure, R. M. and Breuer, Melvin A.
- Subjects
FACTORIZATION ,COMPUTER programming ,OPERATIONS research ,ALGORITHMS ,PROBABILITY theory ,POLYNOMIALS - Abstract
Given a set of expressions which are to be compiled, methods are presented for increasing the efficiency of the object code produced by first factoring the expressions, i.e. finding a set of subexpressions each of which occurs in two or more other expressions or subexpressions. Once all the factors have been ascertained, a sequencing procedure is applied which orders the factors and expressions such that all information is computed in the correct sequence and factors need be retained in memory a minimal amount of time. An assignment algorithm is then executed in order to minimize the total number of temporary storage cells required to hold the results of evaluating the factors. In order to make these techniques computationally feasible, heuristic procedures are applied, and hence global optimal results are not necessarily generated. The factorization algorithms are also applicable to the problem of factoring Boolean switching expressions and of factoring polynomials encountered in symbol manipulating systems. [ABSTRACT FROM AUTHOR]
- Published
- 1969
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