Showing papers on "Graph (abstract data type) published in 1978"

Taxonomy with confidence

Abstract: There are essentially three ways in which four species may be related in a phylogenetic tree graph. It is usual to compute for each of these three possibilities the smallest number of mutations that could have brought about the observed distribution of characteristics among the four species. The graph that minimizes this number is then preferred. In fact, the hypothesis that the graph chosen in this way is correct may be accepted with confidence if the minimum is strong in a sense described here. In principle, the theory could be extended to treat sets of more than four species.

Finding All Spanning Trees of Directed and Undirected Graphs

Abstract: An algorithm for finding all spanning trees (arborescences) of a directed graph is presented. It uses backtracking and a method for detecting bridges based on depth-first search. The time required is $O(V + E + EN)$ and the space is $O(V + E)$, where V, E, and N represent the number of vertices, edges, and spanning trees, respectively. If the graph is undirected, the time decreases to $O(V + E + VN)$, which is optimal to within a constant factor. The previously best-known algorithm for undirected graphs requires time $O(V + E + EN)$.

A new graph product and its spectrum

Abstract: A new graph product is introduced, and the characteristic polynomial of a graph so–formed is given as a function of the characteristic polynomials of the factor graphs. A class of trees produced using this product is shown to be characterized by spectral properties.

An automatic one-way dissection algorithm for irregular finite element problems

Abstract: A formal definition of a nested dissection ordering of the graph of a general sparse symmetric matrix A is given. After introducing some preliminary results which provide a direct relationship betw...

A Tutorial and Bibliographical Survey on Graph Grammars

Abstract: In the first section we make some remarks (without going into any details) about the main application fields of graph grammars to motivate their investigation In section 2 and 3 we give a short and informal overview on most of the approaches for sequential and parallel graph grammars known in literature In the last part we introduce some of the modifications and extensions enforced by several applications and give some comments on implementation of graph grammars realized so far

Context-Free Graph Grammars*

Abstract: In this paper we develop a theory of context-free graph grammars. Formal properties of such grammars are proven, with particular attention to graph language recognizability.

Finding Minimal Center-Median Convex Combination Cent-Dian of a Graph

Abstract: The graph median and center problems are well known with numerous possible applications. The first is suitable for locating a facility providing a routine service, by means of minimizing the average distance of customers to it. The second is appropriate for emergency services where the objective is to have the furthest customer as near as possible to the center. In reality a combination of both, usually antagonistic, goals is common. This paper presents a procedure to locate a facility on a graph, such that a convex combination of the median and the center objective functions is minimized. The term “cent-dian” is coined for this point of the graph. Since it is usually difficult to assign precise weights to the two objectives, when they are convexly combined, the procedure generates the cent-dians for all possible combinations. Finally, an equivalent median problem on an expanded graph is presented.

Parallel Generation of Maps: Developmental Systems for Cell Layers

Abstract: In this paper we extend parallel string generating systems (string L-systems) to parallel map generating systems(BPMOL-systems). The main distinguishing feature of of these constructs is that they generate map patterns by rewriting the graph of the map directly, and not its dual graph. These systems and their languages and sequences are illustrated in particular by applying them to the development of epidermal cell layers in which hexagonal arrays of cells are generated from previous hexagonal arrays.

The argos image understanding system.

Abstract: : ARGOS is an image understanding system. It builds a three-dimensional model of the task domain and uses hypothesized two-dimensional views of the model to label images. It currently achieves less than 20% error by area when labeling real-world (city of Pittsburgh) photographs with a knowledge base of over fifty objects. In addition, the system can determine the angle of view around the city with approximately 40 degrees of error. The labeling technique used by ARGOS is called Locus search. Locus is a non-backtracking graph search technique in which a beam of near-miss alternatives around the best path are extended in parallel through the graph. After the graph has been searched in breadth-first order, the beam of possibilities is examined in reverse order to extract a near-optimal path. This path defines a labeling of the image and is only sub-optimal because of the pruning heuristics used in the beam creation. This thesis formulates image understanding as a problem of search; shows how Locus search can be used to label images; describes the many sources of knowledge used in the interpretation; shows how knowledge represented as a network can be used to constrain the search; explores extensions to the use of knowledge; and presents the experimental results of ARGOS. Its main contributions are the demonstration that Locus search can be used for image understanding and the exploration of issues involved in this use.

Covering a Graph by Circuits

Abstract: A circuit cover is a set of circuits which cover all the edges of a graph; its length is the sum of the lengths of the circuits. In analyzing irrigation systems it is sometimes necessary to find a short circuit cover. It is shown that every bridge-free connected undirected graph with n vertices and e edges has a circuit cover the length of which is less than or equal to e+2nlogn. A probabilistic algorithm for finding such a cover is presented; its expected running time is 0(n2), independent of the input graph. This constitutes an example of solving a graph-theoretical problem by a probabilistic algorithm — the class of algorithms introduced by Rabin.

Programmed Graph Grammars

Abstract: Let [enum], [exp-i] and [pr-i] denote the class of recursively enumerable, typ-i expression and typ-i programmed graph languages respectively. The following hierarchy is known from [5]:

Fragment Search in Acyclic Structures

Abstract: A graph theoretical algorithm is described which allows a search for fragments in acyclic structures. Although the topic discussed in the paper is of limited immediate use, it provides a basis for atom-by-atom matching which may be practical as a large number of unproductive matchings are eliminated from consideration. The approach is based on the concept of atom codes which register the number of neighbors one, two, and more bonds apart. Atom codes provide a means of storing information on a structure (i.e., connectivity) without an explicit use of atom labels. Atom codes also permit assignment of multiple labels to individual vertices based on some specified rules or prescribed properties.

A new signal flowgraph formulation of symbolic network functions

Abstract: Symbolic topological analysis of the closed primitive signal flowgraph corresponding to a linear active or passive network having an edge admittance matrix is considered. First, necessary and sufficient conditions for the occurence of term cancellation in Mason's formula for the graph determinant are established. Then, a new signal flowgraph topological formula for the graph determinant in which no term cancellation occurs is proved. A computer program to implement the new formula is described. It is shown that this program is more efficient than existing programs based on Mason's formula.

An Efficient Simple Algorithm for Fault Tree Automatic Synthesis from the Reliability Graph

Abstract: A simple efficient algorithm for the automatic construction of fault trees concerning complex 2-state, non series-parallel systems is given. The approach begins with the probabilistic graph of the system and results in a suitable form of fault tree that can be used in any available method of numerical evaluation. The technique is simple enough to treat operator failures or environmental effects if they are properly included in the reliability graph. Furthermore it is possible to evaluate the effects of additional redundancies, so making possible an optimization of system reliability.

Interactive Space Layout: A Graph Theoretical Approach

Abstract: This paper proposes an interactive programming approach to the solution of architectural space layout problems. The paper incorporates a brief discussion of some of the problems inherent in existing space layout techniques which may be overcome by the proposed approach. In the suggested computer program, the architectural plan is divided into 3 hierarchical levels of abstract representation; namely, the Graph, The Bubble Diagram, and The Schematic Plan. It is shown how the generation of alternatives at each of these levels is achieved through computer-designer interface. Finally, a representative sample of the questions which may be generated by the interactive system is set forth.

Geometric Dilution of Precision

Abstract: A graph is developed which gives geometric dilution for fixes obtained hyperbolically using information received from three stations. Only bearings from the user to the stations are needed. The approach can be characterized as oriented to the user rather than to system development and is particularly valuable in assessing station choices in redundant systems such as Omega. Dilution is shown to be minor even if all bearings are in the same semi-circle provided the central station is on a nearly central bearing.

On the Characterization of Balancing Processes of Social Systems and the Derivation of the Minimal Balancing Processes

Abstract: The psychological notion of cognitive balance by Cartwright and Harary offers a well-organized mode for consideration of systems theoretic approaches to social problems. The balancing processes of a social system, which transform an unbalanced system to a balanced one by changing the cognitive relations, are characterized in terms of signed graphs. First, the characterization of the balancing processes of the whole system is reduced to the characterization of each subsystem, which is obtained by block decomposition of the whole system. Second, the characterization is made in two different ways according to the planarity of the graph structure of the systems. For systems with planar graph structure, the characterization is effectively made by introducing the notion of dual graph. For systems with general graph structure, the balancing processes are characterized in terms of adjacency matrices. In each case, an efficient algorithm which derives the minimal balancing processes is presented. Finally, a quantitative approach incorporating the relative importance of each relation is examined.

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

On the eulericity of a graph

Abstract: The eulericity ϵ(G) of a bridgeless graph G is defined as the least number of eulerian subgraphs of G which together cover the lines of G. A 1–1 correspondence is shown to exist between the k‐tuples of eulerian subgraphs of G and the proper flows (mod2) on a given network based on G. The inequality ϵ(G) ⩽ 3 them follows from a result of Jaeger.

Order preserving embeddings of aographs

Abstract: We call an oriented graph which does not have any directed cycles an aograph. In this paper we discuss the problem of embedding an aograph on a surface in an order preserving fashion. The general problem is motivated by recent research involving partially ordered sets with planar Hasse diagrams.