Showing papers on "Graph (abstract data type) published in 1975"

Design of cellular production systems A graph-theoretic approach

Abstract: SUMMARY A method is presented for forming machine cells while implementing group technology. Information derived from the route cards of the components is analysed and the situation is represented in the form of a graph whose vertices correspond to the machines and whose edges represent the relationships created between the machines by the components using them. For finding the cells a graph partitioning approach is suggested and developed. Results obtained from testing the method using actual data are also presented.

Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees

Abstract: Backtrack algorithms for listing certain kinds of subgraphs of a graph are described and analyzed. Included are algorithms for listing all spanning trees, all cycles, all simple cycles, or all of c...

Anti-Ramsey theorems

Abstract: Let c be an edge-colouring of the complete n-graph Kn with m colours. A totally multicoloured (TMC) subgraph of Kn (with respect to c) is a graph G⊆Kn such that no two edges of G have the same colour. Let H be a graph with less than n vertices. If m is sufficiently large then there is in Kn a TMC subgraph isomorphic to H. Let f(n,H) denote the maximal number m such that there is an m-colouring of Kn without a TMC-subgraph isomorphic to H. Put d=min(χ(H−e),e∈E(H))−1. It is shown that f(n,H)/(n2) converges to 1−1/d for n→∞. An analogous result is proved for uniform hypergraphs. If, especially, H is a complete graph Kp, the extremal colouring is, for every n, uniquely determined (up to isomorphisms); it is closely related to the Turan graph (with p−1 colour-classes). The problem of determining f(n,H) is also discussed in more detail in the case when H is a path or a circuit, and in the case of a path an explicit formula is given, holding for n sufficiently large.

A Preliminary Evaluation of the Critical Path Method for Scheduling Tasks on Multiprocessor Systems

Abstract: The problem of scheduling tasks on a system of independent identical processors is discussed and the performance of a suboptimal method is evaluated. The computation is modeled by an acyclic directed graph G(T,<), where node set T represents the set of tasks to be completed and edge set < defines the precedence between tasks. The objective is to minimize the finishing time of the computation graph. Known theoretical results are reviewed and a general branch-and-bound algorithm for finding optimal solutions is presented. The schedules produced by a simple critical path priority method are shown to be near optimal for randomly generated computation graphs.

Algorithmic aspects of vertex elimination

Abstract: We consider a graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric and unsymmetric systems of linear equations. We discuss good algorithms for finding elimination orderings, showing that a generalization of breadth-first search, called lexicographic search, can be used to find perfect orderings in 0(n+e) time and minimal orderings in 0(ne) time, if the problem graph is undirected and has n vertices and e edges. We also give efficient (though slower) algorithms for generating such orderings on directed graphs. We claim that the minimum ordering problem for directed graphs is NP-complete, and conjecture that it is also NP-complete for undirected graphs. We include a brief discussion of the relation of elimination to transitive closure and discuss some unresolved, more general, issues.

Induction of concepts in the predicate calculus

Abstract: Positive and negative instances of a concept are assumed to be described by a conjunction of literals in the predicate calculus, with terms limited to constants and universally quantified variables. A graph representation of a conjunction of literals, called a "product graph", is introduced. It is desirable to merge positive instances by generalization, while maintaining discrimination against negative instances. This is accomplished by an induction procedure which operates on the product graph form of these positive and negative instances. The correctness of the procedure is proven, together with several related results of direct practical significance. This work is directed to the goal of providing a formal model for the inductive processes which are observed in artificial intelligence studies in specialized areas.

A Clustering and Data-Reorganizing Algorithm

Abstract: A clustering and data-reorganizing algorithm based on the concept of the shortest spanning path of a graph is given. This algorithm can be used to reorganize and/or cluster a large file of data.

On non-linear lower bounds in computational complexity

Abstract: The purpose of this paper is to explore the possibility that purely graph-theoretic reasons may account for the superlinear complexity of wide classes of computational problems. The results are therefore of two kinds: reductions to graph theoretic conjectures on the one hand, and graph theoretic results on the other. We show that the graph of any algorithm for any one of a number of arithmetic problems (e.g. polynomial multiplication, discrete Fourier transforms, matrix multiplication) must have properties closely related to concentration networks.

An Algorithm for Finding a Minimal Equivalent Graph of a Digraph

Abstract: It lS found that Moyles and Thompson's algorithm contains some mistakes. An efficmnt algorLthm for finding a mlmmal eqmvalent graph (MEG) is presented The algorithm proceeds with the following steps First, all the strongly connected (s c ) components are found. Then the set of vertmes is reordered such that the set of vertices in an s c component is ordered by consecutive integers The rows and columns of the adjacency matrix are permuted accordingly Then an MEG for each s c. component is found Finally, the parallel and the superfluous edges are removed

A Flow-Graph Formula for the Stationary Distribution of a Markov Chain

Abstract: It is shown that a stationary distribution of a regular Markov chain can be obtained directly from its transition graph. The technique is similar to signal flow-graph methods, however, it uses trees of the graph rather than loops. The proof is direct and simple.

Graph Theory in Chemistry II. Graph-Theoretical Description of Heteroconjugated Molecules

Abstract: Abstract The Sachs' formula which relates the structure of a (vertex-and edge) -weighted graph and its characteristic polynomial is given. Weighted graphs are used to represent conjugated molecules containing the variety of heteroatoms and heterobonds. Vertices and edges in such molecular graphs have different weights following the deviation of the corresponding (Hiickel) Coulomb and resonance integrals from the standard (benzene) values.

Structured descriptions of complex curved objects for recognition and visual memory.

Abstract: : Description and recognition of three-dimensional objects from range data obtained by a laser triangulation technique are described. A complex object is described by decomposition into sub-parts and relations of these sub-parts. The individual parts are described by generalized cones, which are defined by a space curve known as the axis, and arbitrary shaped normal cross-sections along this axis. Techniques for segmenting an object into sub-parts and generating structured, symbolic, graph like descriptions are described. These symbolic descriptions are matched with stored descriptions and the best match is picked for recognition. A limited amount of indexing capability exists to efficiently retrieve a sub-class of similar objects from the models stored in the memory. Indexing is a necessity if a large number of visual models is to be used.

Networks of Automata: Some Applications

Abstract: Parallel web automata (PWA?a generalization of cellular arrays to arbitrary graph structures?are defined It is shown that such automata make poor acceptors (ie, they are not good recognizers of their own graph structures) However, they can be used to perform parallel local pattern matching (with respect to patterns of bounded size) on themselves, so that they have potential usefulness as models for ``semantic memory'' They can also be used to find greatest compatible sets of graph labelings subject to given local constraints; this problem arises, for example, in the analysis of scenes containing three-dimensional objects

Path delays in communication networks

Abstract: A communication network is modelled by a weighted graph. The vertices of the graph represent stations with storage capabilities, while the edges of the graph represent communication channels (or other information processing media). Channel capacity weights are assigned to the edges of the network. The network is assumed to operate in a store-and-forward manner, so that when a channel is busy the messages directed into it are stored at the station, joining there a queue which is governed by a first-come first-served service discipline.

Boolesche Minimalpolynome und Überdeckungsprobleme

Abstract: The main difficulty in finding minimal Boolean polynomials for given switching functions comes from the evaluation of the table of prime implicants. We show the following results Finally we make some remarks about the complexity of algorithms, which--given the graph of a switching function--find a minimal polynomial of this function.

Representation of process synchronization

Abstract: There is presently no natural, convenient way to represent synchronization between communicating processes. Two dimensional graph models seem to offer the most natural representations, and of these the Petri net is perhaps the most basic. The author has been working on graph models similar to Petri nets, stressing the ease and convenience of the model as a descriptive device rather than attempting to prove properties such as liveness and safeness. It is shown that Petri nets are incapable of representing some simple and interesting synchronization problems such as reader-writer problems. Recent work has been directed towards the identification of modifications to graph models to overcome such dificiencies.

A problem reduction model for non independent subproblems

Abstract: A hypergraph model is introduced, which besides including the AND/OR graph and state space graph models as particulars, is adequate for problem solving tasks involving non independent subproblems. The hypergraph model is shown to be grounded on a nonstandard notion of conjunction such that the truth of a conjunction does not necessarily imply the truth of the conjuncts. A hypergraph search algorithm is given and shown to be equivalent to a resolution-based theorem prover in a first order logic augmented with the special conjunction. A characterization is given of the class of problems requiring the full descriptive power of our model. The class includes problems involving resources, plan formation, simplification of predicate logic programs.

The maximum size of an independent set in a nonplanar graph

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From dynamic programming to search algorithms with functional costs

Abstract: In this paper we approach, using artificial intelligence methods, the problem of finding a minimal-cost path in a functionally weighted graph, i.e a graph with monotone cost functions associated with the arcs This problem is important since solving any system of functional equations in a general dynamic programming formulation can be shown equivalent to it. A general heuristic search algorithm with estimate is given, which is a nontrivial extension of algorithm A. by Hart, Nilsson and Raphael. Putting some constraints on cost functions and on the estimate, this algorithm can be simplified until the classical version, with additive cost functions, is reached.

Power system dynamic studies for improved stability and minimum rotor heating via graph-theoretic modelling of a dual-excited synchronous generator

Abstract: A systematic approach based on linear graph theory is suggested for linear and non-linear state model formulation of a system comprising of a dual-excited synchronous generator, connected to an infinite bus through a transmission line, and controlled by voltage regulator, angle regulator and a speed governor. Viewing the system as an interconnection of five simple subsystems, each being represented in isolation by a directed terminal graph and a set of terminal equations, leads to the generation of a system graph. A minimal state characterization is easily obtained through selecting a maximal forest, getting constraint equations therefrom, and substituting them in suitably arranged terminal equations. The method is applicable in general for any complex system. Besides presenting some of the computed results from the model thus formulated, for comparison with the experimental data available in the literature, investigations in this paper are further directed towards studies aimed at improving the stability regions to their maximum limit and cutting down the rotor copper losses to a minimum level. The effect of system operation in these modes on the relative choice of the three controller parameters is discussed with the help of various parameter-plane stability-limit loci plots.

Topological Model for a Three-Phase Converter

Abstract: The purpose of this article is to develop an efficient model for the analysis of a three-phase converter. An algorithm for the generation of a modified proper tree and fundamental cutset matrix from a network graph is developed, which utilizes much less computer storage space and computation time compared to the classical methods. A three-phase rectifier bridge with its associated protective circuits is considered and the results obtained from the developed technique are discussed.