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Showing papers on "Graph (abstract data type) published in 1988"


Journal ArticleDOI
TL;DR: An algorithm is presented that generates all maximal independent sets of a graph in lexicographic order, with only polynomial delay between the output of two successive independent sets, unless P=NP.

862 citations


Journal ArticleDOI
TL;DR: The development of the concept attributed adjacency graph (AAG) for the recognition of machined features from a 3D boundary representation of a solid is presented.
Abstract: The internal representation of the solid modeller provides a description of parts which when used directly is useful for automation of the process planning function. So that the CAD model can be used to provide the information required for manufacturing, techniques to improve machine understanding of the part as required for manufacturing are needed. This paper presents the development of the concept attributed adjacency graph (AAG) for the recognition of machined features from a 3D boundary representation of a solid. Current implementation of the feature recogniser is limited to polyhedral features such as pockets, slots, steps, blind steps, blind slots, and polyhedral holes. Sample results that show the capabilities of the system are presented.

720 citations


Journal ArticleDOI
03 Jan 1988
TL;DR: The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures.
Abstract: The state of the art in automatic graph drawing is reviewed, with special attention to the readability of information system diagrams. Existing results in the literature are compared, and a comprehensive algorithmic approach to the problem is proposed. The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures. Several applications of GIOTTO, a graphic tool that embodies the aforementioned facility, are shown. >

463 citations


Journal ArticleDOI
TL;DR: Sehwa can find the minimum-cost design, the highest performance design, and other designs between these two in the design space and executes within minutes, for problems of practical size, on a VAX 11/750.
Abstract: A set of techniques for the synthesis of pipelined data paths is described, and Sehwa, a program that performs such synthesis, is presented. The task includes the generation of data paths from a data-flow graph along with a clocking scheme that overlaps execution of multiple tasks. Some design examples are given. Sehwa can find the minimum-cost design, the highest performance design, and other designs between these two in the design space. Sehwa is written in Franz Lisp and executes within minutes, for problems of practical size, on a VAX 11/750. >

405 citations


01 Jan 1988
TL;DR: A survey of the growing body of theory concerned with parallel algorithms and the complexity of parallel computation, which considers the parallel random-access machine (PRAM), in which it is assumed that each processor has random access in unit time to any cell of a global memory.
Abstract: This paper is a survey of the growing body of theory concerned with parallel algorithms and the complexity of parallel computation The principal computation that we consider is the parallel random-access machine (PRAM), in which it is assumed that each processor has random access in unit time to any cell of a global memory This model permits the logical structure of parallel computation to be studied in a context divorced from issues of interprocessor communication Section 2 surveys efficient parallel algorithms for bookkeeping operations such as compacting an array by squeezing out its "dead" elements, for evaluating algebraic expressions, for searching a graph and decomposing it into various kinds of components, and for sorting, merging and selection These algorithms are typically completely different from the best sequential algorithms for the same problems, and their discovery has required the creation of a new set of paradigms for the construction of parallel algorithms Section 3 studies the relationships among several variants of the PRAM model which differ in their implementation of concurrent reading and/or concurrent writing, presents lower bounds on the time to solve certain elementary problems on various kinds of P RAMs, and compares the PRAM with other models such as bounded-fan-in and unbounded-fan-in circuits, alternating Turing machines and vector machines Section 3 also introduces NC, a hierarchy of problems solvable by deterministic algorithms that operate in polylog time using a polynomial-bounded number of processors Section 4 discusses specific problems within NC Among the problems shown to lie at low levels within this hierarchy are the basic arithmetic operations, transitive closure and Boolean matrix multiplication, the computation of the determinant, the rank an d inverse of a matrix, the evaluation of certain classes of straight-line programs and the construction of a maximal independent set of vertices in a graph Section 4 also discusses the randomized version of NC, and gives fast randomized parallel algorithm s for problems such as finding a maximum matching in a graph Section 4 concludes by exhibiting several problems that are complete in the sequential complexity class P with respect to logspace reducibility, and hence unlikely to lie in NC

383 citations


Journal ArticleDOI
TL;DR: This paper examines a class of asymmetrical multi-depot vehicle routing problems and location-routing problems, under capacity or maximum cost restrictions, by using an appropriate graph representation, and then a graph extension.
Abstract: This paper examines a class of asymmetrical multi-depot vehicle routing problems and location-routing problems, under capacity or maximum cost restrictions. By using an appropriate graph representation, and then a graph extension, the problems are transformed into equivalent constrained assignment problems. Optimal solutions are then found by means of a branch and bound tree. Problems involving up to 80 nodes can be solved without difficulty.

368 citations


Journal ArticleDOI
TL;DR: Eight algorithms which solve the shortest path tree problem on directed graphs are presented, together with the results of wide-ranging experimentation designed to compare their relative performances on different graph topologies.
Abstract: Theshortest path problem is considered from a computational point of view. Eight algorithms which solve theshortest path tree problem on directed graphs are presented, together with the results of wide-ranging experimentation designed to compare their relative performances on different graph topologies. The focus of this paper is on the implementation of the different data structures used in the algorithms. A "Pidgin Pascal" description of the algorithms is given, containing enough details to allow for almost direct implementation in any programming language. In addition, Fortran codes of the algorithms and of the graph generators used in the experimentation are provided on the diskette.

364 citations


Journal ArticleDOI
TL;DR: This work formalizes a notion of loading information into connectionist networks that characterizes the training of feed-forward neural networks and introduces a perspective on shallow networks, called the Support Cone Interaction (SCI) graph, which is helpful in distinguishing tractable from intractable subcases.

221 citations


Journal ArticleDOI
TL;DR: A method is presented for explicitly representing dimensions, tolerances, and geometric features in solid models in a graph structure called an object graph that provides an important foundation for higher-level application programs to automate tolerance analysis and synthesis.
Abstract: A method is presented for explicitly representing dimensions, tolerances, and geometric features in solid models. The method combines CSG and boundary representations in a graph structure called an object graph. Dimensions are represented by a relative position operator. The method can automatically translate changes in dimensional values into corresponding changes in geometry and topology. The representation provides an important foundation for higher-level application programs to automate tolerance analysis and synthesis. The implementation of a prototype interactive polyhedral modeler based on this representation is presented. >

185 citations


Proceedings ArticleDOI
13 Jun 1988
TL;DR: The test results from the measurement of sample programs show that the knowledge of the critical path in a program's execution helps users identify performance problems and better understand the behavior of a program.
Abstract: The authors present the design, implementation, and testing of the critical path analysis technique using the IPS performance measurement tool for parallel and distributed programs. They create a precedence graph of a program's activities (program activity graph) with the data collected during the execution of a program. The critical path, the longest path in the program activity graph, represents the sequence of the program activities that take the longest time to execute. Various algorithms are developed to track the critical path from this graph. The events in this path are associated with the entities in the source program, and the statistical results are displayed on the basis of the hierarchical structure of the IPS. The test results from the measurement of sample programs show that the knowledge of the critical path in a program's execution helps users identify performance problems and better understand the behavior of a program. >

160 citations


Journal ArticleDOI
TL;DR: DAG is a program that draws directed graphs by reading a list of noeds and edges, computing a layout and then writing a PIC or PostScript description of a picture, which works best on directed acyclic graphs.
Abstract: DAG is a program that draws directed graphs by reading a list of noeds and edges, computing a layout and then writing a PIC or PostScript description of a picture. Optional drawing instructions specify the way nodes are drawn, attach labels and control spacing. DAG works best on directed acyclic graphs, which are often used to represent hierarchical relationships. For example, here is a drawing of a graph from J. W. Forrester's book, World Dynamics (Wright-Allen, Cambridge, MA, 1971), which took 1.63 CPU seconds to draw using a VAX-8650.

Journal ArticleDOI
David Callahan1
01 Jun 1988
TL;DR: A method for interprocedural data flow analysis which is powerful enough to express flowsensitive problems but fast enough to apply to very large programs is discussed.
Abstract: This paper discusses a method for interprocedural data flow analysis which is powerful enough to express flowsensitive problems but fast enough to apply to very large programs. While such information could be applied toward standard program optimizations, the research described here is directed toward software tools for parallel programming, in which it is crucial. Many of the recent “supercomputers” can be roughly characterized as shared memory multi-processors. These include top-of-the-line systems from Cray Research and IBM, as well as multi-processor computers developed and successfully marketed by many younger companies. Development of efficient, correct programs on these machines presents new challenges to the designers of compilers, debuggers, and programming environments. Powerful analysis mechanisms have been developed for understanding the structure of programs. One such mechanism, data dependence analysis, has been evolving for many years. The product of data dependence analysis is a dota dependence gmph, a directed multi-graph that describes the interactions of program components through shared memory. Such a graph has been shown useful for a variety of applications from vectorization and parallelization to compiler management of locality. Another application of the data dependence graph is as an aid to static debugging of parallel programs. PTOOL [4] is a software system developed at Rice University to help programmers understand parallel programs. It is within this context that we at Rice have learned of the importance of interprocedural data flow analysis. I will briefly describe the PTOOL system and explain the kind of interprocedural information valuable in such an environment. PTOOL is designed to help locate interactions between

Patent
05 Jul 1988
TL;DR: In this article, a single instruction stream multiple data steam data flow signal processor and a method for implementing macro data flow control is presented, in which a plurality of data processors have contentionless access to global memory data Data processing tasks for the data processors, such as primitive executions together with graph scheduling processes, are developed asynchronously and in parallel from a command program and a macro flow control graph.
Abstract: A single instruction stream multiple data steam data flow signal processor and method for implementing macro data flow control, in which a plurality of data processors have contentionless access to global memory data Data processing tasks for the data processors, such as primitive executions together with graph scheduling processes, are developed asynchronously and in parallel from a command program and a macro data flow control graph

01 Jan 1988
TL;DR: This paper develops a program for computing reachability in a finite directed graph, and defines a procedure reachable that, given a node x and a graph g, will compute the set of nodes that can be reached from x.
Abstract: Perhaps the most important way in which Forsythe is more general than Algol is in its provision of objects, which are a powerful tool for data abstraction. One can write abstract programs in which various kinds of data are realized by types of objects, and then encapsulate the representation of the data, and the expression of primitive operations in terms of this representation, in declarators for the objects. To illustrate this style of programming, we will develop a program for computing reachability in a finite directed graph. Specifically, we will define a procedure reachable that, given a node x and a graph g, will compute the set of nodes that can be reached from x. Throughout most of this development we will assume that "node" is a new data type; eventually we will see how this assumption can be eliminated. Then we can define a "set" to be an object denoting a finite set of nodes, whose fields are procedures for manipulating the denoted set:

Journal ArticleDOI
TL;DR: A neural network model is presented in which each neuron performs a threshold logic function that always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 whenoperating in a fully parallel mode.
Abstract: A neural network model is presented in which each neuron performs a threshold logic function. The model always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 when operating in a fully parallel mode. This property is the basis for the potential applications of the model, such as associative memory devices and combinatorial optimization. The two convergence theorems (for serial and fully parallel modes of operation) are reviewed, and a general convergence theorem is presented that unifies the two known cases. New relations between the neural network model and the problem of finding a minimum cut in a graph are obtained. >

Proceedings ArticleDOI
24 Oct 1988
TL;DR: A general framework for the study of a broad class of communication problems is developed based on a recent analysis of the communication complexity of graph connectivity, which makes use of combinatorial lattice theory.
Abstract: A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory. >

Journal ArticleDOI
TL;DR: In this article, an O(n)-approximation algorithm was developed to construct a rectangular dual of ann-vertex planar triangulated graphs, where n is the number of vertices.
Abstract: We develop anO(n) algorithm to construct a rectangular dual of ann-vertex planar triangulated graph.

Proceedings ArticleDOI
18 Apr 1988
TL;DR: An algorithm for processing the semantic relationship graph to discover whether potential inference aggregation problems exist and the use of set theory and the addition of set operations to the DBMS to permit the description of aggregation detection queries are presented.
Abstract: The author identifies inference aggregation and cardinality aggregation as two distinct aspects of the aggregation problem. He develops the concept of a semantic relationship graph to describe the relationships between data and then presents inference aggregation as the problem of finding alternative paths between vertices on the graph. He presents an algorithm for processing the semantic relationship graph to discover whether potential inference aggregation problems exist. A method of detecting some aggregation conditions within the database management system (DBMS) is presented that uses the normal DBMS query language and adds additional catalytic data to the DBMS to permit a query to make the inference. The author also suggests the use of set theory to describe aggregation conditions and the addition of set operations to the DBMS to permit the description of aggregation detection queries. >

Journal ArticleDOI
TL;DR: This work improves the bounds for N(t, b, k) obtained by Fredman and Komlos and introduces a new non-existence bound based on an extension of graph entropy to hypergraphs.
Abstract: A set of sequences of length t from a b-element alphabet is called k-separated if for every k-tuple of the sequences there exists a coordinate in which they all differ. The problem of finding, for fixed t, b, and k, the largest size N(t, b, k) of a k-separated set of sequences is equivalent to finding the minimum size of a (b, k)-family of perfect hash functions for a set of a given size. We shall improve the bounds for N(t, b, k) obtained by Fredman and Komlos [1]. Korner [2] has shown that the proof in [1] can be reduced to an application of the sub-additivity of graph entropy [3]. He also pointed out that this sub-additivity yields a method to prove non-existence bounds for graph covering problems. Our new non-existence bound is based on an extension of graph entropy to hypergraphs.

Journal ArticleDOI
01 Mar 1988
TL;DR: It is shown that the SAXPY, GAXPY and DOT algorithms of Dongarra, Gustavson and Karp, as well as parallel versions of the LDMt, LDLt, Doolittle and Cholesky algorithms, can be classified into four task graph models.
Abstract: This paper introduces a graph-theoretic approach to analyse the performances of several parallel Gaussian-like triangularization algorithms on an MIMD computer. We show that the SAXPY, GAXPY and DOT algorithms of Dongarra, Gustavson and Karp, as well as parallel versions of the LDMt, LDLt, Doolittle and Cholesky algorithms, can be classified into four task graph models. We derive new complexity results and compare the asymptotic performances of these parallel versions.


Journal ArticleDOI
TL;DR: An off-road vehicle with a suspension system that has eight closed loops is used to illustrate the parallel processor algorithm and to investigate parallel processing speed-up and overhead.
Abstract: A high speed dynamic simulation algorithm that exploits emerging parallel processor computer technology is presented. Medium grain parallelism is defined by the graph structure of a mechanism and the recursive algorithm derived in parts I and II of this paper, for both open and closed loop systems. An off-road vehicle with a suspension system that has eight closed loops is used to illustrate the parallel processor algorithm. A shared memory multiprocessor is used to implement the algorithm and to investigate parallel processing speed-up and overhead. Real-time simulation of a ground vehicle is demonstrated.

Journal ArticleDOI
TL;DR: This paper presents a software architecture and a graph-based framework for developing knowledge-based model management systems that enable a model management system to create composite models automatically.
Abstract: This paper presents a software architecture and a graph-based framework for developing knowledge-based model management systems. The architecture consists of three major components: a model utilization subsystem, a modeling subsystem, and an inference engine. The core of the system is the inference engine that applies the graph-based framework to drive the processes of model integration and selection. The graph-based framework includes a model representation scheme and reasoning mechanisms. The representation scheme depicts a set of data as a node, a set of functions as an edge, and a basic model as a combination of two nodes and one connecting edge. Based on this scheme, mechanisms for model integration and selection are discussed. These mechanisms enable a model management system to create composite models automatically. A prototype implemented in PROLOG is also presented to demonstrate the graph-based framework.

Proceedings ArticleDOI
24 Jul 1988
TL;DR: This proposal shows how to map combinational optimization problems, including graph K-partitioning, vertex cover, maximum independent set, maximum clique, number partitioning, and maximum matching, and reports that performance results are quite encouraging.
Abstract: The ability to map and solve a number of interesting problems on neural networks motivates a proposal for using neural networks as a highly parallel model for general-purpose computing. The author review this proposal, showing how to map combinational optimization problems, including graph K-partitioning, vertex cover, maximum independent set, maximum clique, number partitioning, and maximum matching. They report that performance results are quite encouraging; the solutions for graph partitioning and task allocation problems are comparable to those obtained using heuristics and the running times are significantly lower than those required using simulated annealing. >

Journal ArticleDOI
TL;DR: Two methods are given that use combinations of nodes to enumerate all minimal cutsets of a general acyclic directed graph and four rules are given for deletion of those combinations that yield redundant and nonminimal subsets.
Abstract: Two methods are given that use combinations of nodes to enumerate all minimal cutsets. One simply has to enumerate all combinations of orders 1 to N-3 of nodes from 2 to N-1, where N is the total number of nodes. Collecting only those symbols of links of first row of adjacency matrix and in the rows given in a combination that are not in the columns of the combination, a cutset of an acyclic directed graph having all adjacent nodes is obtained. To obtain the cutsets of a general acyclic directed graph, four rules are given for deletion of those combinations that yield redundant and nonminimal subsets. The rules provide a reduced set of combinations, which then gives rise to minimal cutsets of a general graph. Three examples illustrate the algorithms. >

Journal ArticleDOI
TL;DR: In this article, Pach's number was used to verify the triangle-free graph of the bipartite forbidden graph, which is a triangle free graph with a triangle vertex.

Patent
16 Sep 1988
TL;DR: In this paper, an interface system allows a user to select and control colors used in graphic images generated by a computer system The interface system employs graphical representations of the hue, chroma, and lightness combinations capable of being rendered by computer graphics systems.
Abstract: An interface system allows a user to select and control colors used in graphic images generated by a computer system The interface system employs graphical representations of the hue, chroma, and lightness combinations capable of being rendered by a computer graphics system In a preferred embodiment, the graphical representation includes a one-dimensional graph (40) depicting the range of hues and a two-dimensional graph (42) depicting the range of chroma and value combinations available for a selected hue The graphical representations are preferably rendered in accordance with a Hue-Value-Chroma ("HVC") color space (90) having a high degree of perceptual uniformity

Journal ArticleDOI
TL;DR: A system that performs automated concept acquisition from examples and has been specially designed to work in noisy environments is presented and several criteria are proposed for evaluating the acquired knowledge.
Abstract: A system that performs automated concept acquisition from examples and has been specially designed to work in noisy environments is presented. The learning methodology is aimed at the target problem of finding discriminant descriptions of a given set of concepts and uses both examples and counterexamples. The learned knowledge is expressed in the form of production rules, organized into separate clusters, linked together in a graph structure. Knowledge extraction is guided by a top-down control strategy, through a process of specialization. The system also utilizes a technique of problem reduction to contain the computational complexity. Several criteria are proposed for evaluating the acquired knowledge. The methodology has been tested on a problem in the field of speech recognition and the experimental results obtained are reported and discussed. >

Proceedings ArticleDOI
Pravin M. Vaidya1
01 Jan 1988
TL;DR: A set of 2 points on the plane induces a complete weighted undirected graph as follows: the points are the vertices of the graph and the weight of an edge between any two points is the distance between the points under some metric.
Abstract: A set of 2n points on the plane induces a complete weighted undirected graph as follows: The points are the vertices of the graph and the weight of an edge between any two points is the distance between the points under some metric. We study the problem of finding a minimum weight complete matching (MWCM) in such a graph. We give an O(n23 (logn)4) algorithm for finding an MWCM in such a graph, for the L1 (manhattan), the L2 (euclidean), and the L∞ metrics. We also study the bipartite version of the problem, where half the points are painted with one color and the other half are painted with another color, and the restriction is that a point of one color may be matched only to a point of another color. We present an O(n2.5 logn) algorithm for the bipartite version, for the L1, L2, and L∞, metrics. The running time for the bipartite version can be further improved to O(n2 (logn)3) for the L1 and L∞ metrics.

Book ChapterDOI
TL;DR: A new graph termed the sphere-of-influence graph is proposed as a primal sketch intended to capture the low-level perceptual structure of visual scenes consisting of dot patterns and can be computed efficiently in 0(n log n) time.
Abstract: A new graph termed the sphere-of-influence graph is proposed as a primal sketch intended to capture the low-level perceptual structure of visual scenes consisting of dot patterns. This graph suffers from none of the serious drawbacks of previous methods and for a pattern consisting of n dots, can be computed efficiently in 0(n log n) time.