Showing papers on "Graph (abstract data type) published in 1986"

AND/OR graph representation of assembly plans

Abstract: This paper presents a compact representation of all possible assembly plans of a given product using AND/OR graphs. Such a representation forms the basis for efficient planning algorithms which enable an increase in assembly system flexibility by allowing an intelligent robot to pick a course of action according to instantaneous conditions. Two applications are discussed: the selection of the best assembly plan (off-line planning), and opportunistic scheduling (online planning). An example of an assembly with four parts illustrates the use of the AND/OR graph representation to find the best assembly plan based on weighing of operations according to complexity of manipulation and stability of subassemblies. In practice, a generic search algorithm, such as the AO* may be used to find this plan. The scheduling efficiency using this representation is compared to fixed sequence and precedence graph representations. The AND/OR graph consistently reduces the average number of operations.

Fractional cascading: I. A data structuring technique

Abstract: In computational geometry many search problems and range queries can be solved by performing an iterative search for the same key in separate ordered lists. In this paper we show that, if these ordered lists can be put in a one-to-one correspondence with the nodes of a graph of degreed so that the iterative search always proceeds along edges of that graph, then we can do much better than the obvious sequence of binary searches. Without expanding the storage by more than a constant factor, we can build a data-structure, called afractional cascading structure, in which all original searches after the first can be carried out at only logd extra cost per search. Several results related to the dynamization of this structure are also presented. A companion paper gives numerous applications of this technique to geometric problems.

Constructing a perfect matching is in random NC

Abstract: We show that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomial-bounded number of processors. We also show that several related problems lie in Random NC. These include:

Planning of minimum-time trajectories for robot arms

Abstract: The minimum-time path for a robot arm has been a long standing and unsolved problem of considerable interest. We present a general solution to this problem which involves joint-space tessellation, a dynamic time-scaling algorithm, and a graph search. The solution incorporates full dynamics of movement and actuator constraints, and can easily be extended for joint limits and workspace obstacles. It was found that optimal paths tend to be nearly straight lines in joint space. We discuss implementation difficulties due to the tessellation and to combinatorial proliferation of paths.

A graph-theoretical representation of PL-manifolds — A survey on crystallizations

Abstract: This is a survey of the techniques and results developed by M. Pezzana and his group, which includes, besides the authors, A. Cavicchioli, P. Bandieri and A Donati. The original concept is that of “contracted triangulation”, which was introduced with the main goal of finding a “minimal” atlas for topological manifolds ([P1 1968], [P2 1974], [P3 1974], [FG2 1979]). Only later did the possibility of deducing a graph-theoretical tool — the crystallization — for representing P.L. manifolds occur as a major aspect of the theory ([P4 1975], [F1 1976]). This leads to an application of graph theory to P.L. topology, which seems not to have been explored before. Recently, other authors outside Italy have independently become interested in this subject. For the sake of conciseness, definitions and statements often appear in a form other than that of the quoted references.

Traversal recursion: a practical approach to supporting recursive applications

Abstract: Many capabilities that are needed for recursive applications in engineering and project management are not well supported by the usual formulations of recursion. We identify a class of recursions called “traversal recursions” (which model traversals of a directed graph) that have two important properties they can supply the necessary capabilities and efficient processing algorithms have been defined for them. First we present a taxonomy of traversal recursions based on properties of the recursion on graph structure and on unusual types of metadata. This taxonomy is exploited to identify solvable recursions and to select an execution algorithm. We show how graph traversal can sometimes outperform the more general iteration algorithm. Finally we show how a conventional query optimizer architecture can be extended to handle recursive queries and views.

A Formal Definition of Data Flow Graph Models

Abstract: In this paper, a new model for parallel computations and parallel computer systems that is based on data flow principles is presented. Uninterpreted data flow graphs can be used to model computer systems including data driven and parallel processors. A data flow graph is defined to be a bipartite graph with actors and links as the two vertex classes. Actors can be considered similar to transitions in Petri nets, and links similar to places. The nondeterministic nature of uninterpreted data flow graphs necessitates the derivation of liveness conditions.

On unreliability polynomials and graph connectivity in reliable network synthesis

Abstract: The analysis and synthesis of reliable large-scale networks typically involve a graph theoretic model. We give a survey of the graph theoretic notions which are relevant to the synthesis problem. It is shown how a number of unsolved graph extremal problems relate to the synthesis question.

Tutorial introduction to the algebraic approach of graph grammars

Abstract: This tutorial introduction is intended to provide an intuitive understanding of the general format of the graph grammar mechanism underlying the algebraic approach. We point out the essential role of the gluing construction and discuss basic constructions in connection with sequential and parallel independence of derivations and what to do in the case of sequential resp. parallel dependence.

An Optimal Solution Method for Large-Scale Multiple Traveling Salesmen Problems

Abstract: We develop an efficient branch-and-bound based method for solving the Multiple Traveling Salesman Problem, and develop lower bounds through a Lagrangean relaxation that requires computing a degree-constrained minimal spanning tree. A subgradient optimization procedure updates the Lagrange multipliers. We use fast sensitivity analysis techniques to increase the underlying graph sparsity and reduce the problem size. The algorithm was tested on 416 problems with up to 500 cities and 10 salesmen. We also present computational results on different data sets and parameters in order to identify the major factors that influence the performance of the developed code.

Minimal representation of directed hypergraphs

Abstract: In this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed. Various concepts of minimal representations of directed hypergraphs (called minimal equivalent hypergraphs) are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs. In particular, we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph (number of hyperarcs, number of adjacency lists required for the representation, length of the overall description,etc.). The relationships among the various concepts of minimality are discussed and their computational properties are analyzed. In order to derive such results, a graph representation of hypergraphs is introduced.

Minimal spanning tree: A new approach for studying order and disorder

Abstract: We develop a new approach for studying order and disorder in sets of particles. This approach is based on a graph constructed from the set of points locating the positions of the particles. This graph, which is called the minimal spanning tree, allows us to deduce two parameters, namely, the average edge length $m$ and the standard deviation $\ensuremath{\sigma}$, which are characteristic of the repartition to be studied. The method is applied to particles of an aggregated lithium thin film deposited on a dielectric substrate. These particles are found to be partially ordered. The use of a diagram involving both $m$ and $\ensuremath{\sigma}$ turns out to be a powerful tool for the determination of the degree of order in very various systems.

An algorithmic approach to the automated design of parts orienters

Abstract: This paper concerns the design of parts orienters - the dual to the motion planning problem. Two particular paradigms are considered and their abstractions to the computational domain lead to interesting problems in graph pebbling and function composition on finite sets. Polynomial time algorithms are developed for the abstracted problems.

On the Minimum Violations Ranking of a Tournament

Abstract: This paper examines the problem of rank ordering a set of players or objects on the basis of a set of pairwise comparisons arising from a tournament. The criterion for deriving this ranking is to have as few cases as possible where player i is ranked above j while i was actually defeated by j in the tournament. Such a situation is referred to as a violation. The objective, therefore, is to determine the Minimum Violations Ranking MVR. While there are situations where this ranking would be allowed to contain ties among subsets of objects, we will concern ourselves herein with linear ordering no ties. A series of examples are given where this requirement would seem to be appropriate. In order to put the MVR problem into proper perspective we introduce the concept of a distance on the set of tournaments. A set of natural axioms is presented which any such distance measure should obey, and it is proven that in the presence of these axioms a unique such measure exists. It is then shown that the MVR problem is equivalent to the minimum distance problem, which can be represented in several forms-in particular as a problem of determining the minimum feedback edge set in a graph and as a mixed integer generalized network problem. This opens up a wide scope of possible solution procedures for the MVR problem. An optimal algorithm is presented along with computational results. In addition, various heuristics are discussed including an improved heuristic referred to as the Iterated Kendall method.

An O(2 0.304n ) Algorithm for Solving Maximum Independent Set Problem

Abstract: A faster algorithm for finding a maximum independent set in a graph is presented. The algorithm is an improved version of the one by Tarjan and Trojanowski [7]. A technique to further accelerate this algorithm is also described.

Graph Grammars with Application Conditions

Abstract: The algebraic approach of graph grammars is extended by a very general notion of application conditions which can be defined separately for each production. This extended approach is applied to a small library system in order to show the flexibility of this concept for the design of systems in computer science and related areas. In addition to the general concept we study some special cases of graph grammars with application conditions with respect to their generative power. Finally we state some facts how to extend known results in the algebraic theory of graph grammars to the case with application conditions.

Updating business chart data by editing the chart

Abstract: A method of updating business chart data by editing the business chart is disclosed. The chart is displayed using predefined data. A draw graph object of the business chart is selected for editing. When the editing action is completed, a check is made to determine whether the action on the business chart destroyed the relationship between the chart and the predefined data. If it did and if the user has selected the two-way editing mode, the predefined data is updated to reflect the edited chart.

Set theoretic approaches to graph grammars

Abstract: This paper sketches the approaches of a certain branch of graph grammars mainly studied at Erlangen, Osnabruck, Koblenz and Aachen, West Germany. It is named set theoretic, or expression, or algorithmic approach of graph grammars, because its mathematical base is elementary set theory, expressions are used to denote embedding transformations, and the question of applicability and implementation always was regarded of equal importance as theoretical results.

Parallel Inversion of Sparse Matrices.

Abstract: This paper presents a parallel algorithm for obtaining the inverse of a large, nonsingular symmetric matrix A of dimension nxn. The inversion method proposed is based on the triangular factors of A. The task of obtaining the "sparse inverse' of A is represented by a directed acyclic graph. The relation between the triangulation graph and the sparse inversion graph is given. The algorithm and the graph for the full inversion of A is also given. It is shown that for any sparse symmetric matrix, and assuming enough processors are available, the full inverse of the matrix can be calculated in the same amount of time as the sparse inverse. For ideally sparse matrices (such as tridiagonal matrices) the order of computation required in both cases is of order log2n. For full matrices the order of computation is n log2n. Claims are substantiated using test data from several power systems.

Data base locking

Abstract: A data base system is disclosed in which records are locked out during record changing by using a dynamically generated directed acyclic graph of the records. The edges of the graph, stored in the records themselves, point toward a "root" record representing multiply-shared information. An application to the assignment of telephone facilities to telephone subscribers is also described. A transaction list is maintained to identify locked out records previously locked out during the same transaction.

Hierarchical reasoning: simulating complex processes over multiple levels of abstraction

Abstract: This thesis describes a method for simulating processes over multiple levels of abstraction. There has been recent work with respect to data, object, and problem-solving abstraction, however, abstraction in simulation has not been adequately explored. We define a process as a hierarchy of distinct production rule sets that interface to each other so that abstraction levels may be bridged where desired. In this way, the process may be studied at abstraction levels that are appropriate for the specific task:notions of qualitative and quantitative simulation are integrated to form a complete process description. The advantages to such a description are increased control, computational efficiency and selective reporting of simulation results. Within the framework of hierarchical reasoning, we will concentrate on presenting the primary concept of process abstraction. A Common Lisp implementation of the hierarchical reasoning theory called HIRES is presented. HIRES allows the user to reason in a hierarchical fashion by relating certain facets of the simulation to levels of abstraction specified in terms of actions, objects, reports, and time. The user is free to reason about a process over multiple levels by weaving through the levels either manually or via automatically controlled specifications. Capabilities exist in HIRES to facilitate the creation of graph-based abstraction levels. For instance, the analyst can create continuous system models (CSMP), petri net models, scripts, or generic graph models that define the process model at a given level. We present a four-level elevator system and a two-level "dining philosophers" simulation to demonstrate the efficacy of process abstraction.

Hummingbird isolegs in an experimental system

Abstract: Optimal foraging theory was first looked upon as a tool to study the evolution of niches in community ecology. Isoleg theory is being developed to reestablish it as such a tool. Isoleg theories are maps of isolegs in a graph whose axes are population densities. There are two kinds of isolegs: some are lines of equal optimal behavior in the graph; others mark threshold combinations of densities past which sudden shifts in behavior should occur. A technique for determining whether isolegs exist is described and applied to hummingbird data. These data were collected experimentally in the field expressly to test one isoleg model. All three species of hummingbird exhibited at least one of the sudden-shift type of isoleg. Their behaviors map onto the density graph in the predicted portions of the graph with only one exception. The data also support the prediction that behavior in the field is disjunct, i.e. subject to substantial, abrupt, discontinuous changes produced by very small continuous changes in a control variable. Some evidence for continuous control was also found, but it is ambiguous. Theory predicts that the two forms of control should be found together in some optimal systems.

A Best-First Search Algorithm for Optimal PLA Folding

Abstract: In this paper we propose a new algorithm for optimal PLA folding based on a graph theoretic formulation. An efficient best-first search (BFS) algorithm is presented which finds a near-optimal PLA folding. The proposed algorithm first constructs the longest paths on the associated disjoint graph generated from the PLA personality matrix, and then extracts the ordered folding sets from the constructed paths. The algorithm is shown to be effective for most test cases.

Is parallelism already concurrency? Part 1: Derivations in graph grammars

Abstract: The aim of this paper is to outline the support the theory of graph grammars offers to deal with parallelism and concurrency. The considerations in Part 1 are based on derivations in graph grammars (using a simple, but general framework). Sequentialization and parallelization of derivation steps are studied. From the point of view of concurrency, these constructions induce an equivalence on derivations. It turns out that each equivalence class is uniquely represented by a canonical derivation, which is minimal with respect to a delay index. Part 2 deals with a kind of non-sequential processes in graph grammars (overcoming the sequentiality of derivations).