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Showing papers on "Graph (abstract data type) published in 1969"



Journal ArticleDOI
TL;DR: Yet another set of dimensionless variables is offered that have the advantage of the Blok groups, that all results can be plotted on a single graph, but in addition one group is of secondary impo...
Abstract: Yet another set of dimensionless variables is offered. These have the advantage of the Blok groups, that all results can be plotted on a single graph, but in addition one group is of secondary impo...

40 citations


Journal ArticleDOI
TL;DR: The following problem is considered: Given a data base which can be manipulated simultaneously by more than one process, what are the rules for synchronization which will maximize the amount of parallel activity allowed?
Abstract: The following problem is considered: Given a data base which can be manipulated simultaneously by more than one process, what are the rules for synchronization which will maximize the amount of parallel activity allowed. It is assumed that the data base can be represented as a graph. An example of such a data base is a hierarchy of directories for an on-line file system. Methods for synchronization of processes are examined; their validity is discussed and their performance compared.

40 citations


Journal ArticleDOI
TL;DR: The purpose of this paper is to develop an analytic foundation for the determination of whether a mathematical model and its desired computations are "well-posed" in order to help alleviate the software problems associated with the simulation of complex large-scale systems by heterogeneous mathematical models involving several hundred dimensions.
Abstract: The purpose of this paper is to develop an analytic foundation for the determination of whether a mathematical model and its desired computations are "well-posed" in order to help alleviate the software problems associated with the simulation of complex large-scale systems by heterogeneous mathematical models involving several hundred dimensions. The problem is approached by providing a rigorous basis for the commonplace notion of constraint. Four distinct viewpoints of the mathematical model are established: 1) the set theoretic relation space; 2) the family of submodels; 3) the bipartite graph, which provides topological insight; and 4) the constraint matrix. Fundamental definitions of mathematical model consistency, computational allowability, and extrinsic and intrinsic constraint are established on a set theory basis. Correspondences are proved between the topological properties of a model's graph and its constraint properties. Variables located in different connected components of a graph are always mutually consistent, but computations performed on them are never allowable. If a model graph of universal relations has a tree structure, then all its variables are mutually consistent. Detailed treatment of special relation classes will be given in Parts II and III.

36 citations



Journal ArticleDOI
TL;DR: This paper discusses essential difficulties in calculating mean path lengths on a directed graph model of computations and efficient approximations to mean processing time (mean path length) of programs in such an environment are given.
Abstract: This paper discusses essential difficulties in calculating mean path lengths on a directed graph model of computations. This study was part of a larger study of a priori scheduling of computer programs in a parallel processing environment. Efficient approximations to mean processing time (mean path length) of programs in such an environment are given.

29 citations


Journal ArticleDOI
01 Jan 1969

26 citations


Journal ArticleDOI
TL;DR: A line initialization procedure such that the line can easily be balanced optimally and the minimum cycle time or assembly time can be computed easily from a certain graph, and a corresponding Gantt diagram determined.
Abstract: This paper considers three kinds of assembly-line disciplines: assembly lines without parallel subassemblies, lines with parallel subassemblies, and single-product assembly lines. To each such discipline there corresponds a line balancing problem. For the second and third disciplines, feasible but not necessarily optimal balances are characterized in terms of the directed graph defining the line. For any feasible balance, the minimum cycle time or assembly time can be computed easily from a certain graph, and a corresponding Gantt diagram determined. For the case of lines with parallel subassemblies, the paper gives a line initialization procedure such that, after initialization, the line can easily be balanced optimally.

24 citations


Journal ArticleDOI
TL;DR: An efficient algorithm for finding a minimum-weight generalized matching in a weighted bipartite graph is presented and it is shown that it can be used to solve effectively the well known transportation problem of integer programming where the objective function is convex-separable.
Abstract: This paper presents an efficient algorithm for finding a minimum-weight generalized matching in a weighted bipartite graph. Computational evidence is given that indicates that the time required to find a least-cost assignment of n jobs to n workers goes roughly as n2 for 10 ≦ n ≦ 50. It is shown that this algorithm can be used to solve effectively the well known transportation problem of integer programming where the objective function is convex-separable. Finally, the paper gives an algorithm that applies the same concept to a graph that is not necessarily bipartite.

23 citations


Journal ArticleDOI
Bennett Fox1
TL;DR: This note presents an efficient method for the solution of the flow-circulation problem, the basis for which is a search for a way to route flow so that the cost-time trade-off is optimal.
Abstract: In the treatment of routing problems, other authors have used column generators to introduce, into the basis of the master problem, the solution that corresponds to a cycle in a graph with minimal cost-to-time ratio This subproblem is of independent interest and corresponds to deterministic Markov renewal programming; this note presents an efficient method for its solution, intuitive basis for which is a search for a way to route flow so that the cost-time trade-off is optimal This flow-circulation problem is solved parametrically by the out-of-kilter algorithm

21 citations


Journal ArticleDOI
01 Apr 1969
TL;DR: An algorithm is presented to enumerate all circuits of a linear graph that is suitable for computerization and does not require a large computer memory.
Abstract: An algorithm is presented to enumerate all circuits of a linear graph The method is suitable for computerization and does not require a large computer memory The application of the procedure to some other enumeration problems is discussed

Journal ArticleDOI
TL;DR: The problem of solving sequential Boolean equations is shown to be equivalent to the problem of finding whether there exists a path on a labeled graph for every sequence of labels.
Abstract: The problem of solving sequential Boolean equations is shown to be equivalent to the problem of finding whether there exists a path on a labeled graph for every sequence of labels. Algorithms are given for testing whether a solution exists, and if a solution with a finite delay exists. In case of existence of solutions the algorithms provide them.


Proceedings ArticleDOI
01 Jan 1969
TL;DR: A computer-aided topological layout of components and wiring in integrated circuits will be presented based on a new kind of graph which accounts for all technological restrictions, as well as possibilities.
Abstract: A computer-aided topological layout of components and wiring in integrated circuits will presented based on a new kind of graph which accounts for all technological restrictions, as well as possibilities.


Journal ArticleDOI
TL;DR: In this paper, the concepts of Ordinal Graph and Ordinal Simplex are elaborated and their applicability to some major theoretical problems in sociology is discussed, such as measurement models in sociology.
Abstract: This is the second of two papers on measurement models in sociology. The concepts of Ordinal Graph and Ordinal Simplex are elaborated and their applicability to some major theoretical problems outl...

Journal ArticleDOI
01 Dec 1969
TL;DR: A relationship between the transformations of trees and the corresponding basic loop and cutset matrices is established, which facilitates generation of these matrices with respect to any other or all possible trees of a graph in a routine manner.
Abstract: A relationship between the transformations of trees and the corresponding basic loop and cutset matrices is established, which facilitates generation of these matrices with respect to any other or all possible trees of a graph in a routine manner. These transformation matrices can be set up directly without resorting to a series of elementary transformations. This method of generating the basic loop and cutset matrices is based on the concept of a Lagrangian tree. A method for minimising the number of nonzero entries in a loopset matrix is also discussed. Finally, two new methods for realising a given matrix as a loop or cutset matrix are proposed. These methods of analysis and synthesis will be particularly useful in dealing with complex networks which are commonly encountered in communication systems, electrical and switching networks, and models of many other physical systems.

Journal ArticleDOI
TL;DR: Using a simplified version of the linear graphing techniques employed in computer programming, the decisions and activities of excisional breast surgery are defined and an instructional outline and surgical operation record form are presented.

Journal ArticleDOI
Wai-Kai Chen1
TL;DR: In this article, it is shown that many of the existing techniques in the literature are actually the variants of the Wang algebra formulation, and that they can all be unified, thus, they can be unified.
Abstract: The efficiency with which a complex electrical network may be analysed by a digital computer using topological formulas depends largely upon the efficiency with which the trees and directed trees of the corresponding graph are generated. The problem of efficient generation of trees of a graph has been treated rather extensively in the literature. In this paper it is shown that many of the existing techniques in the literature, seemingly so different in their appearance, are actually the variants of the Wang algebra formulation. Thus, they can all be unified. The unified theory enables one to summarize many of these results systematically and to provide a simple and easy way for their derivations.



Book
01 Aug 1969
TL;DR: A set of primitives to allow graph processing on a list processing system is investigated to provide a method of applying intuitive graph solution techniques to graph oriented computer problems.
Abstract: : A set of primitives to allow graph processing on a list processing system is investigated. The object of the investigation is to provide a method of applying intuitive graph solution techniques to graph oriented computer problems. Applications are presented from several disciplines. (Author)


Journal ArticleDOI
TL;DR: In this paper, the lower limit of detection for a very low-level background (B < 4) has been studied and a graph is presented which allows to find quickly, for a given background, the critical value of the count difference and the lower-limit of detection.

Journal ArticleDOI
TL;DR: A new algorithm is presented for finding all of the descendants of each node of an arbitrary directed linear graph and it is compared with a previously known algorithm and found to be faster for at least one class of implementations.
Abstract: A new algorithm is presented for finding all of the descendants of each node of an arbitrary directed linear graph. The validity of the algorithm is established and it is compared with a previously known algorithm and found to be faster for at least one class of implementations.

Journal ArticleDOI
TL;DR: In this paper, a mathematical expression of the error variance of the addition method is presented and the relation between the precision and the peak-background ratios before and after addition is presented on a graph which may be of help to define the best analytical conditions.


Journal ArticleDOI
TL;DR: In this part of the paper, it is shown that many of the existing techniques can be formulated by matrix algebra and can all be unified.
Abstract: The problem of efficient generation of trees of a graph has been treated rather extensively in the literature. In this part of the paper, it is shown that many of the existing techniques can be formulated by matrix algebra. Thus, they can all be unified. The unified theory enables one to summarize many of these results systematically and to provide a simple and easy way for their derivation. The present Part II may be read independently of Part I (see Chen 1969).

Journal ArticleDOI
TL;DR: It is shown that directed graphs can be used to generate a class of moderately efficient error-correcting codes, which are easily decodable.
Abstract: It is shown that directed graphs can be used to generate a class of moderately efficient error-correcting codes, which are easily decodable.

Dissertation
01 Jan 1969
TL;DR: The problem of partitioning into classes by means of a binary equivalence relation is investigated and several algorithms for determining the number of components in the graph associated with a particular set of elements are constructed and compared.
Abstract: The problem of partitioning into classes by means of a binary equivalence relation is investigated. Several algorithms for determining the number of components in the graph associated with a particular set of elements are constructed and compared. When the classification process operates on independently drawn samples of n distinct elements from a population, the expected number of components is shown to be obtainable recursively for a class of problems called separable; in all cases, estimates are available to reach any desired level of accuracy. Clustering models in Euclidean space are analyzed in detail and asymptotic formulas obtained to complement experiments. Conjectures concerning the general behavior of the expected number of components are presented also. Finally, several computational tools of general interest are improved significantly.