Showing papers on "Graph (abstract data type) published in 1971"

Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters

Abstract: A family of graph-theoretical algorithms based on the minimal spanning tree are capable of detecting several kinds of cluster structure in arbitrary point sets; description of the detected clusters is possible in some cases by extensions of the method. Development of these clustering algorithms was based on examples from two-dimensional space because we wanted to copy the human perception of gestalts or point groupings. On the other hand, all the methods considered apply to higher dimensional spaces and even to general metric spaces. Advantages of these methods include determinacy, easy interpretation of the resulting clusters, conformity to gestalt principles of perceptual organization, and invariance of results under monotone transformations of interpoint distance. Brief discussion is made of the application of cluster detection to taxonomy and the selection of good feature spaces for pattern recognition. Detailed analyses of several planar cluster detection problems are illustrated by text and figures. The well-known Fisher iris data, in four-dimensional space, have been analyzed by these methods also. PL/1 programs to implement the minimal spanning tree methods have been fully debugged.

Depth-first search and linear graph algorithms

Abstract: The value of depth-first search or "backtracking" as a technique for solving graph problems is illustrated by two examples. An algorithm for finding the biconnected components of an undirected graph and an improved version of an algorithm for finding the strongly connected components of a directed graph are presented. The space and time requirements of both algorithms are bounded by k1V + k2E + k3 for some constants k1, k2, and k3, where V is the number of vertices and E is the number of edges of the graph being examined.

A generalized upper bounding algorithm for multicommodity network flow problems

Abstract: : An algorithm for solving min cost or max flow multicommodity flow problems is described. It is a specialization of the simplex method, which takes advantage of the special structure of the multicommodity problem. The only non- graph or non-additive operations in a cycle involve the inverse of a working basis, whose dimension is the number of currently saturated arcs. Efficient relations for updating this inverse are derived.

Optimal location of a single service center of certain types

Abstract: Hakimi has considered the problem of finding an optimal location for a single service center, such as a hospital or a police station. He used a graph theoretic model to represent the region being serviced. The communities are represented by the nodes while the road network is represented by the ares of the graph. In his work, the objective is one of minimizing the maximum of the shortest distances between the vertices and the service center. In the present work, the region being serviced is represented by a convex polygon and communities are spread over the entire region. The objective is to minimize the maximum of Euclidian distances between the service center and any point in the polygon. Two methods of solution presented are (i) a geometric method, and (ii) a quadratic programming formulation. Of these, the geometric method is simpler and more efficient. It is seen that for a class of problems, the geometric method is well suited and very efficient while the graph theoretic method, in general, will give only approximate solutions in spite of the increased efforts involved. But, for a different class of problems, the graph theoretic approach will be more appropriate while the geometric method will provide only approximate solutions though with ease. Finally, some feasible applications of importance are outlined and a few meaningful extensions are indicated.

Signed Digraphs and the Growing Demand for Energy

Abstract: Many problems of society, including those relating to energy use, air pollution and solid-waste disposal, seem amenable to formulation using the techniques of the rapidly growing field of graph the...

A Direct Search Method to Locate Negative Cycles in a Graph

Abstract: A direct search method for locating and tracing negative cycles in a graph is developed based on a property of real, finite sequences. The efficiency of the method and its application for computing minimum cost flows is tested by applying it to solve a series of assignment problems.

Pitch and compass of the speaking voice

Abstract: There are many unsolved problems concerning the linguistic interpretation of intonation curves obtained instrumentally. Among the major ones are (1) How accurate must the instrumental data be to make sure that no linguistically relevant information is missed? (2) Which of the details of the intonation curve are linguistically relevant? (3) How should the graph be scaled? (4) How should the curves be normalized so as to neutralize individual (speaker-dependent) differences?

Interactive horizon building, analysis and editing

Abstract: A programmed computer-human interaction edit method and system for stored seismic horizon data where a two-dimensional graph of such primary horizon data is placed on a data tablet input to the programmed computer and wherein phantom horizon data with reference to coordinates of the graph are generated in response to human contact through the graph to the data tablet for direct input to the computer. Phantom horizon data is stored in a horizon segment file with primary segment data while preventing entry to the horizon segment file of horizon segment data beyond preselected constraints. Responsive to human contact through the graph to the data tablet at the location of phantom horizons and to stored horizon segment data, a first display of segments of two contiguous phantom horizons is produced with all constraint satisfying segments on the graph within a selectable time gate above and below both of the phantom horizons. A second display is produced of depthpoint-RMS velocity profiles for all segments on the first display. A third display is produced of depthpointinterval velocity data for the earth section between the horizons on the first display. Upon deletion of any segment from the first display, automatically and substantially simultaneously the second display and the third display are modified to reflect the removal of data corresponding to any deleted segment.

Computer Diagnosis Using the Blocking Gate Approach

Abstract: In previous papers [3]–[5] the authors considered the application of graph theory to represent and analyze a computer system. From such analysis of the graph (thus the system), we have shown that faults can be detected and located by means of strategically placed test points within the system.

The latencies of correct and incorrect responses in discrimination and detection tasks: Their interpretation in terms of a model based on simple counting

Abstract: A model for two-choice discrimination based on a process of simple counting is described, and two experiments are performed to test the predictions of the model concerning the graph of latency as a function of response proportion. Two main forms of this graph are identified and predicted to arise in different circumstances. The experimental results support the model, and its possible extension to other psychophysical situations, especially signal detection, are then discussed. It is compared with a model derived directly from the detection situation, and the usefulness of testing these models is pointed out.

On the Point-Arboricity of a Graph and its Complement

Abstract: The point-arboricity ρ (G) of a graph G is defined as the minimum number of subsets into which the point set V(G) of G may be partitioned so that each subset induces an acyclic subgraph. Equivalently, the point-arboricity of G may be defined as the least number of colours needed to colour the points of G so that no cycle of G has all of its points coloured the same. This term was introduced by Chartrand, Geller, and Hedetniemi [1], although the concept was first considered by Motzkin [4]. As with the chromatic number of a graph G, which we denote by χ(G), there is no explicit formula for the point-arboricity of a graph. However, Nordhaus and Gaddum [5] have shown that if G is a graph with p points, then

Recognition of hand-printed numerals reduced to graph-representable form

Abstract: A method for reducing handprinted characters to directed graphs is described. When hand-printed characters are reduced to this form, area zoning techniques which have been successfully applied in real time environments can be used. Alternatively, the data in this form can be used to generate descriptions in a simple character-description language.

Unified theory on the generation of trees of a graph Part III. Decomposition and elementary transformations

Abstract: This is the final part of a three-part series on the problem of efficient generation of trees of a graph. In this part of the paper we summarize most of the existing techniques on tree generation that are based on decomposition and elementary tree and co-tree transformations, and provide a unified theory for their derivation.

GIRL–Graph Information Retrieval Language—Design of Syntax

Abstract: Publisher Summary This chapter focuses on the design of syntax—graph information retrieval language (GIRL). GIRL is a programming language, which permits the insertion, retrieval, and deletion of information mapped onto graph structures. The ease with which GIRL traces or dynamically transforms flowchart-like organizations makes the language especially suitable for the symbol manipulation involved in syntactic and semantic network generation and recognition, data and program management systems, and scheduling system simulation. For example, in GIRL, a person can write a compiler–compiler, a personnel background inventory, or a job shop simulator. The basic and immediate requirement for creating GIRL identifiers is that each identifier must be associated with the address of some arbitrary node of the graph under consideration. To segment an input string of GIRL, a person must pose several restrictions on the form of identifiers. A numeral is a type of literal, and a number is a type of symbol. A number-oriented language can deal with non-numeric literals, and a symbol-oriented language can deal with arithmetic operations.

Sensitivity-state modelling for systems with multi-terminal components†

Abstract: The main objective of this paper is to develop procedures to formulate sensitivity-state equations for systems with multi-terminal first-order linear components, whether active or passive, without using equivalent circuit techniques Thereby, the sensitivity-state variables that appear are all directly measureable, with evident advantages when systems are being studied in the laboratory as well as simulated on the digital computer The equations are obtained through a well-documented algorithm for picking the maximally selected formulation forest of the system graph under consideration Using the concepts of state space it is seen that sensitivity functions may be obtained by calculating the responses of a dependent linear model, topologically equivalent to the original, with element values and driving functions determined by partial derivatives of the original system quantities The process of automatic formulation and solution of the two classes of state models for the original and sensitivity systems i

The minimal cost maximum matching of a graph (supplementary remarks)

Abstract: In addition to the preceding paper, it will be shown that (1) the matching problem is closely related to the linear assignment problem and how (2) this property can be taken advantage of for solving the matching problem.

On the length of feedback shift registers

Abstract: A result relating the length of a feedback shift register to the lengths of the cycles in its state transition graph is presented. Specifically, it is shown that, if a state of a feedback shift register is in one cycle of length c1, and another cycle of length c2, then the length of this shift register must be less than c1+c2 − g.c.d. (c1, c2). This result is then shown to be relevant to the problem of realizing sequential machines with feedback shift registers.