Showing papers on "Graph (abstract data type) published in 1979"

The genetic graph: a representation for the evolution of procedural knowledge

Abstract: I shall describe a model of the evolution of rule-structured knowledge that serves as a cornerstone of our development of computer-based coaches. The key idea is a graph structure whose nodes represent rules, and whose links represent various evolutionary relationships such as generalization, correction, and refinement. I shall define this graph and describe a student simulation testbed which we are using to analyze different genetic graph formulations of the reasoning skills required to play an elementary mathematical game.

Constructing the Call Graph of a Program

Abstract: The proliferation of large software systems written in high level programming languages insures the utility of analysis programs which examine interprocedural communications. Often these analysis programs need to reduce the dynamic relations between procedures to a static data representation. This paper presents one such representation, a directed, acyclic graph named the call graph of a program. We delineate the programs representable by an acyclic call graph and present an algorithm for constructing it using the property that its nodes may be linearly ordered. We prove the correctness of the algorithm and discuss the results obtained from an implementation of the algorithm in the PFORT Verifier [1].

Locking and Deadlock Detection in Distributed Data Bases

Abstract: This paper descrbes two protocols for the detection of deadlocks in distributed data bases–a hierarchically organized one and a distributed one. A graph model which depicts the state of execution of all transactions in the system is used by both protocols. A cycle in this graph is a necessary and sufficient condition for a deadlock to exist. Nevertheless, neither protocol requires that the global graph be built and maintained in order for deadlocks to be detected. In the case of the hierarchical protocol, the communications cost can be optimized if the topology of the hierarachy is appropriately chosen.

A Min-Cut Placement Algorithm for General Cell Assemblies Based on a Graph Representation

Abstract: A new placement algorithm for general cell assemblies is presented which combines the ideas of polar graph representation and min-cut placement. First a detailed description of the initial placement procedure is given, then the various methods for placement improvement (rotation, squeezing, reflecting) and global routing are discussed. A sample circuit is used to demonstrate the performance of the algorithms. Results are shown to compare favourably with manually achieved solutions.

Error-correcting coding system

Abstract: A method and apparatus for constructing long error-correcting codes from one or more shorter error-correcting codes, referred to as subcodes, and a bipartite graph. The graph specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes. Lower bounds on the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subcodes. Both the encoders and decoders employed take advantage of the code's explicit decomposition into subcodes to decompose and simplify the associated computational processes. Bounds on the performance of two specific decoding algorithms are established, and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed. The decoders are able to make effective use of probabilistic information supplied by the channel receiver, such as reliability information, without greatly increasing the number of computations required. By a chosen transmission order for the digits that is appropriate for the graph and the subcodes, the code has excellent burst-error correction abilities.

An algorithm for tree-query membership of a distributed query

Abstract: The aim is to process distributed queries ef ficiently. The cost of communications between sites is dominant in processing such queries. It is assumed that the amount of data transferred determines the transmission cost to a large extent. Thus, it is desirable to minimize the amount of transmitted data. Bernstein-and Chiu [2] classified queries into two types: tree and cyclic queries. They defined an operation called semi-join which requires minimal transfer of data between sites. Then they showed that tree queries can always be answered by semi-joins but cyclic queries may not. An algorithm to decide whether a query is cyclic or not was presented in their paper. Their algorithm works when the number of domains in common between any two relations is no more than one. The aim of this paper is to generalize their algorithm. Specifically, we present a conceptionally simple algorithm which decides the type of a query when the number of domains in common between two relations may exceed one. An implementation of the algorithm is outlined. The algorithm runs in 0(max(e,e')) time and O(e) space complexity where e and e' are the number of edges in the transitive closure of the join graph and the query graph respectively.

Assignment of Tasks in a Distributed Processor System with Limited Memory

Abstract: A recently published algorithm shows how to assign modules to a two-processor computer system with distributed execution so as to minimize the total of execution costs and interprocessor communication costs. In this paper we consider the same problem except that one processor has limited memory capacity. Although this problem is NP-complete, techniques based on the Gomory–Hu tree from network flow theory can be applied to instances of the problem to obtain a reduction in complexity. A new technique based on a graph called the inclusive cut graph is shown to be an even more powerful tool. These two techniques can solve some instances of the problem completely; still others are reduced sufficiently to be susceptible to enumerative techniques. In the worst case, the techniques yield no reduction in problem size.

Problem-Solving Models and Search Strategies for Pattern Recognition

Abstract: Noting the major limitations of multivariate statistical classification and syntactic pattern recognition models, this paper presents an overview of some recent work using alternate representations for multistage and nearest neighbor multiclass classification, and for structural analysis and feature extraction. These alternate representations are based on generalizations of state-space and AND/OR graph models and search strategies developed in artificial intelligence (AI). The paper also briefly touches on other current interactions and differences between artificial intelligence and pattern recognition.

Graph Theory and Integer Programming

Abstract: Publisher Summary A very large part of combinatorics deals or can be formulated as to deal with optimization problems in discrete structures. Generally, the constraints and the objective function are linear forms of certain variables that are restricted to integers or, mostly, to 0 and 1. Thus, the combinatorial problem is translated to a linear integer-programming problem. The value of such a translation depends on whether it provides new insight or new methods for the solution. This chapter discusses several most important results in integer programming that have been successfully applied to graph theory and then discusses those fields of graph theory where an integer-programming approach has been most effective. The chapter also discusses many graph theoretical results that have a linear programming flavor but no explicit treatment.

Review and Revocation of Access Privileges Distributed Through Capabilities

Abstract: The problems of review and revocation of access privileges are presented in the context of the systems that use capabilities for the long-term distribution of access privileges An approach that solves both of these problems in their-most general form is presented in this paper The approach requires that a capability propagation graph be maintained in memory spaces associated with subjects (eg, domains, processes, etc) that make copies of the respective capability; the graph remains inaccessible to those subjects, however Parallel processes of the operating system update the graph as the system runs

On Determining the Genus of a Graph in O(v^O(g)) Steps

Abstract: In this paper we present an algorithm which on input a graph G and a positive integer g finds an embedding of G on a surface on genius g, if such an embedding exists. This algorithm runs in (v) O(g) steps where v is the number of vertices of G. We believe that removing the nondiscrete topological definitions (i.e., the notation or differentiability, 2-dimensional surface, etc.) from our formal definitions has a multitude of advantages. First our goal is to produce an algorithm which operates on discrete machines and thus at some point we must remove these notions anyway. Secondly, demonstrations on proofs in the amalgam of graph theory and topology have been riddled with flaws (e.g., 4-color theorem, planarity algorithms, Jordan curve theorem), and which, no doubt, this paper also suffers. The hope is that a combinatorial proof may transcend these problems. Third, our main goal is not just to draw graphs on “inner tubes” but to understand how graph theory, topology and computational complexity interact. We have kept no definitions sacred and we have redefined the notion of a graph. We have even rewritten Euler's formula.

Recursive data structures in APL

Abstract: A mathematical study of three approaches for defining nested arrays in APL is presented. Theorems exhibiting the relationships between the definitional systems are given and illustrated through graph representations. One of the approaches is used to define an APL array to be a recursive data structure equivalent to a tree structure in which all data is stored at the leaves as homogeneous arrays of numbers and characters. An extension of APL is proposed that includes new primitive functions to manipulate the nesting level of arrays and new operators to assist in the construction of data-driven algorithms.

Survey of results on the maximum genus of a graph

Abstract: Some of the early questions concerning the maximum genus of a graph have now been answered. In this paper we survey the progress made on such problems and present some recent results, outlining proofs for some of the major theorems.

The Schorr-Waite graph marking algorithm

Abstract: An explanation is given of the Schorr-Waite algorithm for marking all nodes of a directed graph that are reachable from one given node, using the axiomatic method.

The graph-theoretic field model—I. Modelling and formulations

Abstract: The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure. This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.

On properties of a well‐known graph or what is your ramsey number?

Abstract: Strictly speaking, the collaboration graph G is really a hypergraph. The oertex set V ( G ) of G is usually taken to be the set of mathematicians. A subset X c V(G) is an edge of G iff there exists a published paper (or book)* which has X as its set of authors. However, for the purposes of this note, we consider G as a graph by replacing each (hyper)edge X by the complete graph K(X) on X. In accordance with the usual conventions for this topic, at most one edge in K(X) will be allowed in any solution of the various extremal problems for G we will consider. We should note that occasionally the restricted graph G* c G is considered in which only papers having exactly two authors are allowed to generate edges [l]. We should say a few words about the notation used in the figures. A solid edge between A and B usually indicates that a paper having A and B as authors has appeared or is about to appear. A dotted line indicates that the paper in question will probably appear (perhaps at present is just a technical report). Other various notations will be described in the text.

Fast parallel processing array algorithms for some graph problems(Preliminary Version)

Abstract: The parallel processing array consists of an n×n array of processors to which a cn2 node directed graph can be input by placing c nodes at every point of the array. It is shown that every one of the following properties of the graph can be computed in order of n steps: (1) to test whether the graph is strongly connected, (2) to mark a node in every strongly connected component, (3) to mark a strong connected component that contains a given node, (4) to mark a simple directed path between a given pair of nodes, and (5) to compute the interconnectivity of the c nodes within every point. As a consequence, several open problems can be solved. For example, any language recognized by a 2-dimensional finite state automaton with 1 pebble can be recognized in order of n steps by a parallel processing array. (It was not even known whether the languages recognized by 2-dimensional finite state automata without pebbles can be recognized in order of n steps by a parallel processing array). Note that a 1 pebble automaton can run for order of n4 steps before accepting an input.