Showing papers on "Graph (abstract data type) published in 1970"

Control flow analysis

Abstract: Any static, global analysis of the expression and data relationships in a program requires a knowledge of the control flow of the program. Since one of the primary reasons for doing such a global analysis in a compiler is to produce optimized programs, control flow analysis has been embedded in many compilers and has been described in several papers. An early paper by Prosser [5] described the use of Boolean matrices (or, more particularly, connectivity matrices) in flow analysis. The use of “dominance” relationships in flow analysis was first introduced by Prosser and much expanded by Lowry and Medlock [6]. References [6,8,9] describe compilers which use various forms of control flow analysis for optimization. Some recent developments in the area are reported in [4] and in [7]. The underlying motivation in all the different types of control flow analysis is the need to codify the flow relationships in the program. The codification may be in connectivity matrices, in predecessor-successor tables, in dominance lists, etc. Whatever the form, the purpose is to facilitate determining what the flow relationships are; in other words to facilitate answering such questions as: is this an inner loop?, if an expression is removed from the loop where can it be correctly and profitably placed?, which variable definitions can affect this use? In this paper the basic control flow relationships are expressed in a directed graph. Various graph constructs are then found and shown to codify interesting global relationships.

An Analysis of Some Graph Theoretical Cluster Techniques

Abstract: Several graph theoretic cluster techniques aimed at the automatic generation of thesauri for information retrieval systems are explored. Experimental cluster analysis is performed on a sample corpus of 2267 documents. A term-term similarity matrix is constructed for the 3950 unique terms used to index the documents. Various threshold values, T, are applied to the similarity matrix to provide a series of binary threshold matrices. The corresponding graph of each binary threshold matrix is used to obtain the term clusters.Three definitions of a cluster are analyzed: (1) the connected components of the threshold matrix; (2) the maximal complete subgraphs of the connected components of the threshold matrix; (3) clusters of the maximal complete subgraphs of the threshold matrix, as described by Gotlieb and Kumar.Algorithms are described and analyzed for obtaining each cluster type. The algorithms are designed to be useful for large document and index collections. Two algorithms have been tested that find maximal complete subgraphs. An algorithm developed by Bierstone offers a significant time improvement over one suggested by Bonner.For threshold levels T ≥ 0.6, basically the same clusters are developed regardless of the cluster definition used. In such situations one need only find the connected components of the graph to develop the clusters.

An efficient search algorithm to find the elementary circuits of a graph

Abstract: A theoretically most efficient search algorithm is presented which uses an exhaustive search to find all of the elementary circuits of a graph. The algorithm can be easily modified to find all of the elementary circuits with a particular attribute such as length. A rigorous proof of the algorithm is given as well as an example of its application. Empirical bounds are presented relating the speed of lhe algorithm to the number of vertices and the number of arcs. The speed is also related to the number of circuits inthe graph to give a relation between speed and complexity. Extensions to undirected and s-graphs are discussed.

On a Homomorphism of the de Bruijn Graph and its Applications to the Design of Feedback Shift Registers

Abstract: A homomorphism of the de Bruijn graph that maps a graph of order n onto one of order n-1 and its applications to the design of nonsingular feedback shift registers are discussed. The properties preserved under this mapping suggest a new design technique whose main advantage is due to the fact that the problem of designing a desired n-stage shift register may be reduced to a problem of order n-1 or less. Among the results obtained is a recursive formula for a feedback function that generates a cycle of maximum length.

Some Basic Definitions in Graph Theory

Abstract: A systematic list of definitions of some basic concepts in graph theory of application to physics is presented. An index, some illustrative theorems, and a brief bibliography are included.

Parsing of Graph-Representable Pictures

Abstract: A syntax-directed picture analysis system based on a formal picture description scheme is described. The system accepts a description of a set of pictures in terms of a grammar generating strings in a picture description language; the grammar is explicitly used to direct the analysis or parse, and to control the calls on pattern classification routines for primitive picture components. Pictures are represented by directed graphs with labeled edges, where the edges denote elementary picture components and the graph connectivity mirrors the picture component connectivity; blank and don't care “patterns” allow the description of simple relations between visible patterns. The bulk of the paper is concerned with the picture parsing algorithm which is an n-dimensional analog of a classical top-down string parser, and an application of an implemented system to the analysis of spark chamber film. The potential benefits of this approach, as demonstrated by the application, include ease of implementation and modification of picture processing systems, and simplification of the pattern recognition problem by automatically taking advantage of contextual information.

Sparsity-Directed Decomposition for Gaussian Elimination on Matrices

Abstract: This is a concise critical survey of the theory and practice relating to the ordered Gaussian elimination on sparse systems. A new method of renumbering by clusters is developed, and its properties described. By establishing a correspondence between matrix patterns and directed graphs, a sequential binary partition is used to decompose the nodes of a graph into clusters. By appropriate ordering of the nodes within each cluster and by selecting clusters, one at a time, both optimal ordering and a useful form of matrix banding are achieved. Some results pertaining to the compatibility between optimal ordering for sparsity and the usual pivoting for numerical accuracy are included.

A technique for generating almost optimal Floyd-Evans productions for precedence grammars

Abstract: A technique is developed for generating almost optimal Floyd-Evans productions given a precedence grammar. A graph formulation is used for the problem of merging productions. The productions generated correspond to the minimum cost inverse-arborescence of that graph. The validity of the technique is demonstrated for weak precedence grammars defined here, but the productions mechanically generated for any precedence grammar can often be modified in such a way that correct, almost optimal parsers are obtained.

How to describe a graph

Abstract: we almost c e r t a i n l y have in mind some s o r t o f diagram, drawing, o r o the r geometr ical r e a l i z a t i o n of t he graph"; and Harary says i n '), p.213, tha t "one p i c t u r e is worth more than t e n thousand words". Hence it i s no t s u r p r i s i n g t o see i n books o r papers on graph theory t h a t most au tho r s p r e f e r drawings t o desc r ip t ions by formulas o r adjacency matrices. D r a w i n g s have of course the advantage o f immedia t e v i sua l i za t ion , but they have a tremendous disadvantage i n t h a t they a r e r a t h e r spaceand timeconsuming.

Methods for the computer-implemented solution of a class of 'floor plan' design problems

Abstract: : The work presented is intended as a case study in computer-implemented design. Its purpose is to illustrate the relationship between the representation chosen for a design problem and the methods developed for solving that problem. A formal class of 'floor plan'-type design problems is defined. In these problems a set of rectangular rooms is specified, and an allowable list of dimensions is given for each room. In addition, a set of required adjacencies between rooms, or between a room and an outside wall of the building, is given. The problem is to produce a rectangular floor plan of a building that contains all of the specified rooms, and that satisfied all of the adjacency and dimension requirements. A linear graph representation for floor plans is developed. This graph is the dual graph of the floor plan, itself treated as a linear graph. Thus, the nodes of the dual graph correspond to rooms, and the edges correspond to adjacencies between rooms. The design methods are implemented in a computer program, GRAMPA, written in IPL-V. Several illustrative problems solved by GRAMPA are discussed. (Author)

The structuring of process optimization

Abstract: The efficiency of process optimization by mathematical programming can be increased by tearing, that is, rearranging the design equations so as to reduce the number of equality constraints. The structure of a system of equations may be depicted as an undirected bipartite graph; algorithm I-T utilizes this graph to determine an order of solution for the equations which requires no tears. If this is impossible, then algorithm II-T uses indexing in conjunction with algorithm I-T to produce an order which minimizes the number of torn equations. This procedure is extended to the problem of minimum recycle parameters, and the two-way interaction between tearing and algebraic simplification is illustrated.

A Universal Arithmetic Building Element (ABE) and Design Methods for Arithmetic Processors

Abstract: The advent of large-scale integration of logic circuits requires the definition of digital computer structure in terms of large functional arrays of logic of very few types. This paper describes a single-package arithmetic processor called the arithmetic building element (ABE). The ABE accepts operands in either conventional or signed-digit radix-r representation and produces signed-digit results, which the ABE can reconvert to conventional form. Radix 16 is chosen for illustrations. Arrays of ABE's may be arranged to implement unit- time parallel addition, all-combinational multiplication, and more complex functions which are presently computed by subroutines. To facilitate such arithmetic design, a graph model is developed which permits a translation of the given arithmetical algorithm into an interconnection diagram of ABE's. The design procedure is illustrated by an array for polynomial evaluation. Speed, cost, and roundoff error of the array are considered. A computer program has been written for the automatic translation of the algorithm graph to an interconnection graph, and for the evaluation of the cost and speed for a given polynomial degree and a given precision requirement.

An Interactive Graph Theory System

Abstract: The medium of computer graphics provides a capability for dealing with pictures in man-machine communication. Graph theory is used to model relationships which are represented by pictures and is therefore an appropriate discipline for the application of an interactive computer graphics system. Previous efforts to solve graph theoretic problems by computer have usually involved specialized programs written in a symbolic assembly language or algebraic compiler language.

The Ensu scoring system in genetic counselling.

Abstract: SUMMARY As a device for systematically computing the posterior probability that a woman is the carrier of an X -linked recessive disorder, a new scoring system has been devised. The information provided by a woman and her male descendants is condensed into an equivalent number of normal sons. Thus if the likelihood ratio of her and her descendants, supposing her a carrier, to that supposing her wild-type is expressible as (1/2)a, the score is a Equivalent Normal Son Units (Ensu). The method, designed in the first place to deal with strictly recessive disorders, is readily extended to the case where the carrier state can be identified with greater or less certainty and the case where other pertinent probabilistic information such as linkage data is available. Tables and a graph are provided which should allow three-digit accuracy, sufficient for all practical purposes.

On the exchange of information

Abstract: There is widespread and increasing interest in moving information between computer installations which may differ in their hardware, software , or their program libraries and data files [1,2,3]. There is general agreement that the task of making a major program written at one installation available for use at another installation is difficult, and is not seriously undertaken without thorough analysis. Yet there seems to be considerable optimism that the problem of accessing a data base at a foreign installation can be solved through development of a "data description language" that would serve to characterize any class of data objects that might be communicated among computer installations [4]. The purpose of this paper is to argue that the general problem of data exchange is no less difficult than the problem of program exchange, and that the concept of a "data description language" is not a solution to the problem. The Problem To express the general problem of data base transfer, consider two contexts within which procedures may be executed so as to accomp]ish computations on behalf of users. Let these be known as context A and 41 context B. By the term "context" we mean the collection of all those factors that determine the detailled course of execution of computations performed by a computer installation. The factors defining a context for execution of a procedure P are normally these: I. The programming language in which P is expressed for presentation to the computer installation. 2. The compiler for the programming language in which P is expressed. 3. The computer hardware in which the compiled form of P is run. 4. The file manipulation and con~nunications services provided by the operating system of the installation. 5. The set of rules used by the installation for binding external references contained in P. 6. The status of catalogs or directories of data and procedures; the files themselves; the user account under which P is executed. A difference in any of these factors may cause the procedure P to have different effect when performed at two installations. Now let us formulate the problem. A data base D has been created by procedures operating in context A. As shown in Figure la, let Q be representative of these procedures. It is desired to make use of D in a distinct context B. We assume that 'Rake use of D"means that a user wishes to carry out …

Notes on combinatorial mathematics: anti-blocking polyhedra

Abstract: : A geometric duality theory of anti-blocking pairs of polyhedra is developed and applied to a number of problems in extremal combinatorics. It is shown that anti-blocking pairs are characterized by a min-max equality, the analogue of the max-flow min-cut equality for blocking pairs of polyhedra, or by a max-max inequality, the analogue of the length-width inequality for blocking pairs of polyhedra. A main combinatorial result is that if A, B are (0,1)- matrices defining an anti-blocking pair of polyhedra, then the min-max equality holds for both ordered pairs A, B and B, A in a strong integer form. This theorem bears on a well-known unsolved problem in graph theory, the perfect graph conjecture, and in fact proves what might be called the 'pluperfect' graph theorem.

Computational Topology for Data Analysis

Abstract: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.

On a Homomorphism of thede Bruijn Graph and ItsApplications totheDesign of Feedback ShiftRegisters

Abstract: AhomomorphismofthedeBruijn graphthatmaps a graphofordern onto one ofordern -1 anditsapplications tothe designofnonsingular feedbackshiftregisters are discussed. The properties preserved underthismappingsuggesta new designtech- niquewhosemainadvantageisduetothefactthattheproblemof designing adesired n-stageshiftregister may bereduced toa problem oforder n -1orless. Amongtheresults obtained isa recursive formula fora feedbackfunction thatgeneratesa cycleofmaximum length. IndexTerms-de Bruijngraphs,designof binarynonsingular feedbackshiftregisters, homomorphism. I. INTRODUCTION

Scheduling to reduce conflict in meetings

Abstract: Conflicts in scheduling can be treated as defining an undirected linear graph independently of the relation of the activities in conflict to additional constraints of time and space Each connected component of such a graph, which can be found by an algorithm described by Gotlieb and Corneil, corresponds to a set of events that must be scheduled at different times

On applications of graph/network theory to problems in communication systems

Abstract: Graph/network theory results are applicable to problems in communications. As a representative example, the node coloring problem in graph theory is applicable to the channel assignment problem in cellular mobile communication systems. The node coloring problem is NP-complete, meaning that optimally solving it is very difficult. Therefore, we use heuristic algorithms for the channel assignment problem. In this case, the graph theory results show the legitimacy of using heuristic techniques. On the other hand, we can directly apply graph theory to communication problems. For example, on contents delivery services in the Internet, we place mirror servers that provide the same contents on the network. Location problems on flow networks are applicable to mirror server allocation problems. In a simple case, we can efficiently solve the problem. In this paper, we concentrate on multi-hop wireless networks and consider the relationship between their problems and the results of graph/network theory.

Circuit, cutset and path enumeration, and other applications of edge-numbering convention

Abstract: New methods employing an edge-numbering convention are proposed for listing all circuits and cutsets of an arbitrary graph, which are an improvement over the ones recently given by Maxwell and Reed. Storage of a master path matrix, whereby the all-path matrix between any two nodes of a given graph can be derived by simple modification, is discussed. A technique for generation of all trees, including a given set of edges and some significant properties of master path matrices, are also discussed. The algorithms proposed are all suitable for computer adoption.

Fuzzy Fault Evaluation In Causal DiagnosticReasoning

Abstract: Causal reasoning is a practical support for model-based diagnosis [1]. The paper addresses the issues of extending diagnostic reasoning based on abductive analysis of causal structures. The extension is aimed at admitting fuzzy characterization of faults; binary evaluation (i.e. faulty/correct) is no longer necessary. The degree of faultyness is expressed with use of basic fuzzy notions. This extension uses a uniform model for representing causal behaviour of diagnosed systems: it has the form of an AND/OR/NOT causal graph allowing for specification of causality types reflecting the basic logical operations [3]. The graph can be used to search for potential (possible) diagnoses. Validation of generated diagnoses is performed by propagation of fuzzy faults upwards the graph [3]. A motivational discussion introducing the presented ideas at an intuitionistic level is presented in brief. Finally, possibilities for further extensions and related work are pointed out.

A graph-theoretic approach to the analysis of international relations:

Abstract: In the usual manner of using a matrix to represent the adjacency relation in a graph, directed graph, or network (see Harary, Norman, and Cartwright, 1965), the i'th row and the i'th column stand for the i'th nation in their sample of 35 nations (as named in Table 1), and the i, j entry of the matrix (in the i'th row and the]'th column) tells the relationship of the i'th nation to thej'th. Thus, in matrix A (Bernstein and Weldon, p. 177), the ij entry, denoted a(ij), is 1 if nation i has a "reciprocal defense relation" with nation j, i $ j, and