Showing papers on "Graph (abstract data type) published in 1968"

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

Abstract: Although the problem of determining the minimum cost path through a graph arises naturally in a number of interesting applications, there has been no underlying theory to guide the development of efficient search procedures. Moreover, there is no adequate conceptual framework within which the various ad hoc search strategies proposed to date can be compared. This paper describes how heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching and demonstrates an optimality property of a class of search strategies.

Scheduling Parallel Computations

Abstract: A model for parallel computations is given as a directed graph in which nodes represent elementary operations, and branches, data channels. The problem considered is the determination of an admissible schedule for such a computation; i.e. for each node determine a sequence of times at which the node initiates its operation. These times must be such that each node, upon initiation, is assured of having the necessary data upon which to operate. Necessary and sufficient conditions that a schedule be admissible are given. The computation rate of a given admissible schedule is defined and is shown to have a limiting value 1/p where p is a parameter dependent upon the cycles in the graph. Thus, the computation cannot proceed at a rate exceeding 1/p. For g ≥ p, the class of all periodic admissible schedules with period g is characterized by the solution space of a certain system of linear inequalities. In particular, then, the maximum computation rate of 1/p is attainable under a periodic admissible schedule with period p. A class of all-integer admissible schedules is given. Finally, an algorithm is given for the determination of the number of initiations of each node in the graph defining a parallel computation. An example for a system of difference equations is given in detail.

A directed graph representation for computer simulation of belief systems

Abstract: A method of representing data structures in the form of a directed graph is described. Such a graph is suitable for the data base of belief systems in particular and of large memory structures in general.

Master circuit matrix

Abstract: The setting up of a master circuit matrix, whereby all possible circuits of any given graph or network with the same, or a smaller, number of nodes can be obtained as a simple modification of the former, is discussed. With the help of such a master matrix, it is also possible to obtain accurately the number of all possible circuits in the given graph, without actually generating them. Besides the flexibility in the choice of circuits it provides for network studies, the enumeration of all circuits should find useful application in other fields, such as operational research, materials management etc. The method actually exploits the inherent symmetry in a complete graph and is also suited for computer adaptation. In the process, a new method of enumerating all possible circuits of a complete graph, and a formula to determine their number, are given. Finally, some important properties of the master circuit matrix are discussed, which include a formula for the number of circuits in which a given combination of edges occurs, a recurrence relationship for the circuit enumeration of different masters, an expression for the number of circuits in a subgraph of a complete graph and a method for setting up a circuit matrix of an arbitrary graph from master B etc.

A new continuous boy-girl growth chart for pediatric office use. A single-sheet graph for all children.

Abstract: * Presented at the 34th Annual Memorial Hospital Research Day, Pawtucket, Rhode Island, November 9, 1966. Address: (A. A. J. and R. A. J.) 765 Broadway, Pawtucket, Rhode Island. As practicing pediatricians, we have deS vised a new and simplified single continuous height and weight growth chart for boys and girls from 0 to Il years. It is designed for routine pediatric office use only. We consolidated the six separate Iowa University and four Children’s Medical Center of Boston 2 infant and children growth charts into a single chart on a single sheet of paper.

Application of unilateral and graph techniques to analysis of linear circuits

Abstract: Extensive research is currently under way in developing methods to solve a linear system of first-order differential equations, and in particular the system of equations associated with computer-oriented circuit design1-20 The methods presented here are based upon topological and graph theory, which is a natural modeling method for networks since an electrical network is a topological arrangement of electrical components The information pertinent to circuit analysis and synthesis can be categorized in two phases: first, the topological arrangement of circuit components, and second, the electrical relations within the components

The coarseness of a graph

Abstract: © Foundation Compositio Mathematica, 1968, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Process for determining the simple cycles of a finite directed graph

Abstract: A machine process based on an algorithm for finding the simple cycles of a finite directed graph wherein each arc of the graph is examined once and only once. Simple cycles are found either when the path of the graph being examined is found to be cyclic or when parts of previously found cycles can be combined with a portion of the path then being examined to form cycles. A general purpose computer program for implementing the algorithm is described.

Enumeration of all cutsets of a graph

Abstract: A technique is presented by means of which all cutsets of a graph can be obtained. From the list of all possible segregations of the vertices of the graph into two complementary sets, those which do not yield cutsets are deleted. The method is suitable for computerization.

A note on the diameter of a graph

Abstract: The distance d(x, y) between vertices x, y of a graph G is the length of the shortest path from x to y in G. The diameter δ(G) of G is the maximum distance between any pair of vertices in G. i.e. δ(G) = max max d(x, y). In this note we obtain an upper bound x ε G y ε G for δ(G) in terms of the numbers of vertices and edges in G. Using this bound it is then shown that for any complement-connected graph G with N vertices where is the complement of G.

Topological formulation of network functions without generation of k-trees.

Abstract: Linear network analysis by topological formulas for derivation of k-tree terms without generation of k-trees of graph

DDA Scaling Graph

Abstract: Finite graph theory is applied to the problem of scaling fixed point Digital Differential Analyzers. The DDA scaling graph is introduced as a representation of the essential scaling information rather than the conventional integrator servo program network. Using the scaling graph, optimal scales are obtained simply, by constructing a maximum distance tree.

The applicability matrix of a syntax-directed parsing processor

Abstract: Some bottom-up syntax-directed parsing processors use a rectangular Boolean matrix called an applicability matrix to determine which rules might be used in the syntax analysis of an input string of terminal (basic) characters of a given language. By constructing a graph derived from the rules of a language specified in Backus Normal Form, and imposing a partial order on the vertices of this graph, it is shown in this paper that the applicability matrix may be partitioned into 2 submatrices, one of which is rectangular, and the other uppertriangular.

Modelling and scheduling of computer programs for parallel processing systems

Abstract: Computer programs which involve large amounts of computation time are targets for analysis to determine two factors; (1)the portions of the program which are most time-consuming, and (2) the effect upon solution time of multiprocessor systems [1].In our automatic modelling system, analysis begins with a working source program written in a language such as FORTRAN. From this source program a graphical representation is prepared. The initial graph represents the program just as it might be processed on a single processor. In this model the flow of control, as explicitly stated by the programmer, is separated from the flow implicit in the language. Data-dependency is also recorded.

Universal connecting networks and the synthesis of canonical sequential circuits

Abstract: The problem is treated of finding for a set of identical processing elements an interconnection structure that achieves a certain richness of interelement communication with only a limited number of actual inter-element connections In graphical terms, this problem is one of finding a universal n-node graph of minimal degree D(n,d) in which every n-node graph of maximum degree d is branchembeddable This problem is solved in both the undirected and directed cases for small values of d and for small values of n - d, and some general properties of D(n,d) are derived Interpretation of a directed universal graph as the state graph of a sequential circuit leads to a canonic form for autonomous non-singular networks--that is, a simple network form that is capable of arbitrary autonomous behavior, the specialization being achieved through the selection of a small amount of internal logic

Growing the trees of a graph

Abstract: An algorithm is described which generates without duplication and with appropriate sign all the trees of a graph containing directed elements. A path-finding algorithm is extended in an application of Mason's method of expansion of paths.