Showing papers on "Graph (abstract data type) published in 1976"

An application of heuristic search methods to edge and contour detection

Abstract: This paper presents a method for detecting edges and contours in noisy pictures. The properties of an edge are embedded in a figure of merit and the edge detection problem becomes the problem of minimizing the given figure of merit. This problem can be represented as a shortest path problem on a graph and can be solved using well-known graph search algorithms. The relations between this representation of the minimization problem and a dynamic programming approach are discussed, showing that the graph search method can lead to substantial improvements in computing time. Moreover, if heuristic search methods are used, the computing time will depend on the amount of noise in the picture. Some experimental results are given; these show how various information about the shape of the contour of an object can be embedded in the figure of merit, thus allowing the extraction of contours from noisy pictures and the separation of touching objects.

A Graph Model for Fault-Tolerant Computing Systems

Abstract: An approach to fault-tolerant design is described in which a computing system S and an algorithm A to be executed by S are both defined by graphs whose nodes represent computing facilities. A is executable by S if A is isomorphic to a subgraph of S.A k-fault is the removal of k nodes (facilities) from S.S is a k-fault tolerant (k-FT) realization of A if A can be executed by S with any k-fault present in S. The problem of designing optimal k-FT systems is considered where A is equated to a 0-FT system. Techniques are described for designing optimal k-FT realizations of single-loop systems; these techniques are related to results in Hamiltonian graph theory. The design of optimal k-FT realizations of certain types of tree systems is also examined. The advantages and disadvantages of the graph model are discussed.

On Algorithms for Enumerating All Circuits of a Graph

Abstract: A brief description and comparison of all known algorithms for enumerating all circuits of a graph is provided, and upper bounds on computation time of many algorithms are derived The vector space

Cliques of a graph-variations on the Bron-Kerbosch algorithm

Abstract: This paper develops a family of algorithms that are variations on the Bron-Kerbosch algorithm for finding all the cliques of a simple undirected graph. The algorithms are developed in a stepwise manner, from a recursive algorithm for generating all combinations of zero or more objects chosen fromN objects. Experimental results are given.

Parallel algorithms for the transitive closure and the connected component problems

Abstract: Parallel programs are presented that determine the transitive closure of a matrix using n3 processors and connected components of an undirected graph using n2 processors. In both cases, the desired results are obtained in time 0(log2n). It is assumed that the processors have access to common memory. Simultaneous access to the same location is permitted for fetch, but not store, instructions.The problem of determining the connected components of a graph using a parallel computer has recently appeared in the literature [1,2]. The result in [1] is based on finding the transitive closure of a matrix in time 0(log2n) which can be done using 0(n3) processors. We show that n2 processors are sufficient to solve the connected component problem in time 0(log2n).We present algorithm CLOSURE that will find the transitive closure of Boolean matrix M [n by n] using n3 processors [numbered P(0,0,0) through P(n−1 ,n−1, n−1)] each of which has local memory and each of which can access common array A [n by n].

Estimation, Identification and Feedback

Abstract: Publisher Summary The analysis of a complex system frequently entails the construction of a signal-flow graph. The nodes of such a graph denote processes and the directed edges denote transformations of the processes, which flow through those edges. In engineering, economic, and biological modeling, the existence and sense of direction of the edges of the signal flow graph are often chosen on a priori grounds. This chapter presents a concept that distinguishes those cases where a unique direction of influence exists between two given processes. This notion is formalized in the definition of feedback-free processes.. The chapter concludes with a description of the applications of the methods presented in economics, power systems, and physiology.

Graph grammars and global program data flow analysis

Abstract: Program structure is defined in terms of a simple graph grammar, the "semi-structured flow graph grammar," which admits many of the control structure extensions suggested for "structured programming." The grammar defines a set of graph reductions which are shown to have the "Finite Church-Rosser (FCR)" property; i.e., when applied in any order to a graph, the limit (when no further reductions are possible) is unique. In particular, if a given graph is generated by the grammar, repeated application of the reductions will result in a single node regardless of the order in which they are applied. This property gives rise to an algorithm that parses a given program flow graph in time linear in the size of the graph. The resulting parse is used in a global data flow analysis algorithm which requires a number of bit-vector steps which is also linear in the size of the given graph.

PAS-II: An Interactive Task-Free Version of an Automatic Protocol Analysis System

Abstract: PAS-II, a computer program which represents a generalized version of an automatic protocol system (PAS-I) is described. PAS-II is a task-free, interactive, modular data analysis sis system for inferring the information processes used by a human from his verbal behavior while solving a problem. The output of the program is a problem behavior graph: a description of the subject's changing knowledge state during problem solving. As an example of system operation the PAS-II analysis of a short cryptarithmetic protocol is presented.

System structure and minimal structural controllability

Abstract: The new concept of "minimal structural controllability" relating to structural controllability is defined and studied. The necessary and sufficient conditions for a multi-input sturctured system to be minimal structurally controllable are given. The results are expressed in both graph theoretical and algebraic statements, where their derivation also provide an alternate proof on structural controllability of multi-input case [1], [2].

A Bound for the Chromatic Number of a Graph

Abstract: (1976). A Bound for the Chromatic Number of a Graph. The American Mathematical Monthly: Vol. 83, No. 4, pp. 265-266.

The Detection of Randomness in Plant Patterns

Abstract: A new technique suitable for the detection of randomness in patterns of plant individuals, based on the properties of the Simplicial graph, is described and shown to be a superior method of analysis to those currently used.

Facilities design with graph theory and strings

Abstract: A facilities design algorithm is developed based upon such graph theory concepts as maximal spanning trees and planar graphs. The upper bound to the demands made by closeness ratings is developed from graph theory. The algorithm lends itself to computer solution minimizing the costs of flow between activities. An alternative approach using strings and the list processing capabilities of computers is suggested. Numerical examples are provided given input in the form of the relationship matrix and working through the block plan layout.

Graph Transformations for Roundoff Analysis

Abstract: When analyzing a numerical algorithm, it is often possible to show that a rounding error at one floating-point operation is equivalent to errors at other operations. In such cases, it can be concluded that no generality is lost if certain operations are considered error-free. Sometimes this conclusion can be reached automatically and inexpensively compared to the cost of the ultimate roundoff analysis. It may be advantageous to use a preprocessor which performs this reduction before other automatic techniques are invoked.In this report we consider a class of elementary rounding error reductions which are most naturally interpreted as graph transformations. This leads to questions concerning heuristics and optimal strategies for the application of these transformations.

A note concerning the connectivity of social networks

Abstract: A simple modification of a method presented by Doreian (1974) adapts it for finding, in a network or “valued graph”, the maximum level paths which do not have cycles or repeated points and which have a specified maximum length.

A new deterministic network reliability measure

Abstract: We introduce and study properties of a new definition of connectivity and reliability which we call “mean connectivity.” The usual definition of cohesion which is used in survivability or reliability analysis is local in that it is the minimum size of an edge cutset. Mean connectivity involves an average time to connectivity, where the average is over random sequences of the edges of a graph. Aside from intuitive appeal, the new definition is shown to have desirable mathematical properties.

Measurement of Influence in Organizations — Critique of the Contol-Graph Method:

Abstract: The "control-graph" is a method for analyzing the distribution of influence in organizations, which has been developed by A.S. Tannenbaum. The technique has certain methodological assumptions and it is shown that these are not valid in the data, which are analysed in this paper. The aim is to discuss the methodological, but not the theoretical problems of the control-graph, and the paper indicates that the resu:ts of previous control graph studies are brought into doubt. Some of the results of the investigation point to the fact that power in organizations has more dimensions and must therefore be taken as too ambiguous when operationalized as in the control graph.

On the analysis and synthesis of active networks containing DVCCS/DVCVS

Abstract: A signal-flow graph approach to the problem of analysis of networks containing resistors, capacitors, and DVCCS/DVCVS is given, and a flexible synthesis procedure is derived.

Applications of graph theory in computer systems

Abstract: Many problem situations in computer systems can be analyzed using models based on directed graphs. The vertices of the graph represent states of the system and the directed arcs represent the transitions between these states. This paper is in two parts. The first introduces the concepts of directed graphs and their representations in computers and presents some basic problems and algorithms. The second part examines the application of graph theory to various areas of computer systems.

Introduction to Singularity Theory with Historical Remarks

Abstract: Naively speaking this map is stable since if we push (or perturb) the graph of the map slightly (as shown by dotted line), the topological pictures of the dotted graph and the solid graph are the same. More rigorously, the dotted curve is just the graph of a reparametrization of f.