Showing papers on "Graph (abstract data type) published in 1980"
TL;DR: In this paper, a new class of models for contingency tables, graphical models, are defined and investigated, which are hierarchical models that can be represented by a simple, undirected graph on as many vertices as the dimension of the corresponding table.
Abstract: We use a close connection between the theory of Markov fields and that of log-linear interaction models for contingency tables to define and investigate a new class of models for such tables, graphical models. These models are hierarchical models that can be represented by a simple, undirected graph on as many vertices as the dimension of the corresponding table. Further all these models can be given an interpretation in terms of conditional independence and the interpretation can be read directly off the graph in the form of a Markov property. The class of graphical models contains that of decomposable models and we give a simple criterion for decomposability of a given graphical model. To some extent we discuss estimation problems and give suggestions for further work.
418 citations
TL;DR: A geometric modeling system that generates a data base in which objects and assemblies are represented by nodes in a graph structure that represents relationships among objects such as part-of, attachment, constraint, and assembly.
Abstract: Very high level languages for describing mechanical assembly require a representation of the geometric and physical properties of 3-D objects including parts, tools, and the assembler itself. This paper describes a geometric modeling system that generates a data base in which objects and assemblies are represented by nodes in a graph structure. The edges of the graph represent relationships among objects such as part-of, attachment, constraint, and assembly. The nodes also store positional relationships between objects and physical properties such as material type. The user designs objects by combining positive and negative parameterized primitive volumes, for example, cubes and cones, which are represented internally as polyhedra. The data base is built by invoking a procedural representation of the primitive volumes, which generates vertex, edge, and surface lists of instances of the volumes. Several applications in the automatic assembly domain have been implemented using the geometric modeling system as a basis.
206 citations
TL;DR: The results are compared with previous work on probabilistic relaxation labeling, and examples are given from the image segmentation domain, to applications of the new scheme in text processing.
Abstract: Let a vector of probabilities be associated with every node of a graph. These probabilities define a random variable representing the possible labels of the node. Probabilities at neighboring nodes are used iteratively to update the probabilities at a given node based on statistical relations among node labels. The results are compared with previous work on probabilistic relaxation labeling, and examples are given from the image segmentation domain. References are also given to applications of the new scheme in text processing.
201 citations
TL;DR: In this article, the ground states of a quenched random Ising spin system with variable concentration of mixed nearest-neighbour exchange couplings +or-J on a square lattice are studied by a new method of graph theory.
Abstract: The ground states of a quenched random Ising spin system with variable concentration of mixed nearest-neighbour exchange couplings +or-J on a square lattice (frustration model) are studied by a new method of graph theory. The search for ground states is mapped into the problem of perfect matching of minimum weight in the graph of frustrated plaquettes, a problem which can be solved by the algorithm of Edmonds. A pedestrian presentation of this elaborated algorithm is given with a discussion of the condition of validity.
143 citations
TL;DR: For a given model graph and pattern on it, the cause of state changes and the manner of their propagation are easily found out by the present approach, which is mainly based on the depth-first search algorithm developed by Tarjan.
117 citations
TL;DR: Two new algorithms are proposed for enumerating all the cutsets or all the s-t cutsets separatmg two spectfied verttces s and t m an undirected graph and how good the performance of the old algorithm is, when a given graph is "dense."
Abstract: Thts paper deals wRh the problem of enumerating all the cutsets or all the s-t cutsets separatmg two spectfied verttces s and t m an undirected graph A vanety of approaches have been proposed for this problem, among which one based on the partmon e ra set of veruces rote two sets is the most effi¢ienL It is first shown that an algorithm of this type has time complexity O((n + m)(n log2#)#), and two new algorithms with ume complexity O((n + m)O + I)) are then proposed One of these new algorithms has space complexity O(nZ), and the other has space complexity O(n + m), where n and m are the numbers of veraces and edges, respectively, and ta ts the number ofs-t cutsets m a given graph The results of some computatmnal experiments are also described. An mvest~gaUon ~s made of the extent to whtch the new algorithms are better, and how good the performance of the old algorithm is, especmlly when a given graph is \"dense,\" t e , 2m/(n(n 1)) _> 0.4.
107 citations
01 Jan 1980
TL;DR: The single machine sequencing problem is considered, in which each job has a processing time and a weight, and there are precedence constraints on the jobs.
Abstract: The single machine sequencing problem is considered, in which each job has a processing time and a weight, and there are precedence constraints on the jobs. The objective is to find a sequence of jobs which minimises the weighted sum of completion times. A new lower bound is derived and used in a branch and bound algorithm. Computational results for up to forty jobs are given.
83 citations
01 Jan 1980
77 citations
TL;DR: In this article, the degree of similarity between molecules is proportional to the distance between points in the corresponding "structure space" obtained by interpreting the entries in molecular path sequences as coordinates inn-dimensional space.
Abstract: The structure similarity and dissimilarity implied in many structure-property and structure-activity relationships has been examined from the graph theoretical point of view. The approach outlined is fundamentally different from generally used schemes in that, rather than seeking a new parametrization which will quantitatively fit observed data and trends,similarities among the skeletal forms and connectivities of the compounds of interest are studied quantitatively. The basis of the method is the assumption that skeletal forms of apparent similarity will yield similar enumerations for a number of graph theoretical invariants. In particular, allpaths within molecular skeletons are enumerated and sequences of path numbers (i.e., the number of paths of different length) are compared. The degree of similarity between molecules is proportional to the distance between points in the corresponding “structure space” obtained by interpreting the entries in molecular path sequences as coordinates inn-dimensional space. As anexample of the use of the concept of structural similarity, structure-activity data relating cerebral dopamine agonist properties for a series of N-substituted 2-aminotetralins are considered. The analysis suggests that the method may find wide application in the field of structure-activity correlations and structure-property studies. The data could be mass spectra, the “fingerprint” regions of infrared spectra, optical rotation and circular dichroism measurements, or any of many not fullyunderstood complex experimental findings suspected of having an inherent structural basis.
70 citations
TL;DR: Previous solution techniques can be reused if the distances in the graph are judiciously redefined and the problem of optimally locating a facility on a graph when one or more other facilities have already been located in theGraph.
Abstract: Previous treatments of location problems on a graph have been confined to the optimum location of a single facility or the simultaneous optimum location of multiple facilities. This paper addresses the problem of optimally locating a facility on a graph when one or more other facilities have already been located in the graph. This paper shows that previous solution techniques can be reused if the distances in the graph are judiciously redefined.
66 citations
01 Apr 1980
TL;DR: The characterization of graph morphisms in terms of the subgraphs of the Cartesian graph product is extended and used to develop algorithms for an optimal graph monomorphism problem.
Abstract: The characterization of graph morphisms in terms of the subgraphs of the Cartesian graph product is extended and used to develop algorithms for an optimal graph monomorphism problem. The objective functional considered is defined as the sum of the weights associated with vertex and arc mappings. A reduction algorithm is proposed to obtain sharp lower bounds on the value of the solution. The lower bounds are used in a branch-and-bound algorithm for the optimal graph monomorphism problem.
Patent•
IBM1
TL;DR: An associative file design method and apparatus are used for automatically generating an integrated data base design structure, with minimal data redundancy, for use in multi-application general purpose digital computing systems.
Abstract: An associative file design method and apparatus are used for automatically generating an integrated data base design structure, with minimal data redundancy, for use in multi-application general purpose digital computing systems. The integrated data base design structure is automatically produced by a programmed digital computer in the form of a report or graph structure which permits the data base designer to design a data base system with minimal data redundancy. The data needed by each application program, i.e., the local data view, is specified with certain constructs. The local data views are checked to ensure that specified rules are followed. The collection of local views is processed on a general purpose digital computer to separate "keys" from "attributes," then to determine "implied" and "essential" associations, and finally to generate the integrated data base graph structure.
TL;DR: A theory of graph-like expressions is developed as far as the basic theoretical result which underlies the remainder of the study of efficient evaluations of expressions, which shows that for a wide class of expressions there are theoretical benefits in allowing graph- like expressions in evaluation algorithms.
15 Jun 1980
TL;DR: A graph grammar is constructed from a given Petri-net so that direct derivation steps in the grammar correspond to firings of transitions in the net, and the well-known dining-philosophers problem is discussed.
Abstract: A graph grammar is constructed from a given Petri-net so that direct derivation steps in the grammar correspond to firings of transitions in the net. This close relationship between Petri-nets and graph grammars allows to compare the concurrency concepts of the two theories. As an illustrating example the well-known dining-philosophers problem is discussed.
TL;DR: In this article, a negative ion model is obtained for daytime conditions by using the signal flow graph technique, which is briefly described and analyzed in terms of transmittances, path gains, and loop gains.
Abstract: Aeronomic systems such as the negative ion chemistry in the D region are characterized by numerous reactions involving positive, negative, and neutral species. Classical solutions of such systems do not necessarily point out the role played by each parameter. When the chemical system is considered as a graph, it is possible to apply the signal flow graph technique, which allows a quantitative evaluation of the various paths and loops. A negative ion model is obtained for daytime conditions by using the signal flow graph technique, which is briefly described. This reference model is analyzed in terms of transmittances, path gains, and loop gains. An arbitrary variation of atomic oxygen and nitric oxide is introduced at a height of 65 km in order to show the induced effects on the negative ions and on the electron concentrations. Variations of the ratio λ between negative ions and electrons are also presented.
TL;DR: In this article, it was shown that the problem of finding a minimum $k$-basis, the $n$-center problem, and the $p$-median problem are NP-complete even in the case of such communication networks as planar graphs with maximum degree 3.
Abstract: It is shown that the problem of finding a minimum $k$-basis, the $n$-center problem, and the $p$-median problem are $NP$-complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal $m$-center problem is also $NP$-complete.
TL;DR: Handwritten words are read by applying hierarchical relaxation labeling procedures to a hierarchical description of the word it reads, which is contextually disambiguated and thus simplified by the application of relaxation procedures.
TL;DR: An efficient algorithm for solving the graph-realization problem by means of PQ -graphs is presented and it is shown that the value of α(ν, k ) is not more than 3 for all practical values of ν and k, so the problem can be solved in a running time almost proportional to ν, the number of nonzero elements of N.
01 Jan 1980
TL;DR: The problem of determining whether a graph has a Hamilton cycle is NP-complete whereas there exists a polynomial algorithm for finding a perfect triangle-free 2-matching if one exists as mentioned in this paper.
Abstract: The problem of determining whether a graph has a Hamilton cycle is NP-complete whereas there exists a polynomial algorithm to determine whether a graph has a perfect 2-matching. These two problems are related to the question of determining whether a graph has a perfect triangle-free 2-matching. We give a polynomial algorithm to answer this question and to find a perfect triangle-free 2-matching if one exists.
TL;DR: In this paper, the relative neighbourhood graph (r.n.g.) of a set of data points is considered from an alternative viewpoint, which leads to properties of the RnG which can be exploited to give faster algorithms, one restricted to use with two-dimensional data and Euclidean distance, and the other being more general.
Abstract: The definition of the relative neighbourhood graph (r.n.g.) of a set of data points is considered from an alternative viewpoint. This leads to properties of the r.n.g. which can be exploited to give faster algorithms, one of which is restricted to use with two-dimensional data and Euclidean distance, and the other being more general.
TL;DR: In this paper, a review of some of the statistical inference problems which have been considered in connection with sampling from a population graph has been presented, along with an overview of the methods used to solve them.
Abstract: Summary Graph models can be used in sample surveys utilizing a known or observable relational structure defined for pairs of units. This review paper gives an overview of some of the statistical inference problems which have been considered in connection with sampling from a population graph.
Patent•
11 Aug 1980TL;DR: In this article, a graphical plot of pressure versus time during pressure build-up in a temporarily closed well is matched to a type-curve on a graph of such curves to determine if the well is fractured, acidified, fissured or damaged.
Abstract: A graphical plot of pressure versus time during pressure build-up in a temporarily closed well is matched to a type-curve on a graph of such curves to determine if the well is fractured, acidified, fissured or damaged.
TL;DR: A general evaluation algorithm of the outermost type is given, and proved to be optimal for a wide class of systems of graph-like expressions.
Proceedings Article•
18 Aug 1980TL;DR: In order to summarize a story it is necessary to access a high level analysis that highlights the story's central concepts, and a technique of memory representation based on affect units appears to provide the necessary foundation for that analysis.
Abstract: In order to summarize a story it is necessary to access a high level analysis that highlights the story's central concepts. A technique of memory representation based on affect units appears to provide the necessary foundation for such an analysis. Affect units are conceptual structures that overlap with each other when a narrative is cohesive. When overlapping intersections are interpreted as arcs in a graph of affect units, the resulting graph encodes the plot of the story. Structural features of the graph then reveal which concepts are central to the story. Affect unit analysis is currently being investigated as a processing strategy for narrative summarization.
TL;DR: It is proposed to define a hierarchical order of the variables of an interdependent system, which is analogous to the hierarchical order given by the reduced graph of a recursive system.
15 Jun 1980
TL;DR: A marked Petri net may be considered as a finite description of an (in general) infinite set of nonsequential processes; thus the process set of a marked net is a graph language.
Abstract: A marked Petri net may be considered as a finite description of an (in general) infinite set of nonsequential processes. Such a process is represented as a labelled graph; thus the process set of a marked net is a graph language. This language is produced by a graph grammar which can be derived from the net. This construction yields a bijection between the set of marked Petri nets and a distinguished class of graph grammars.