Showing papers on "Adjacency list published in 1998"

Automatic recognition of interacting machining features based on minimal condition subgraph

Abstract: This paper presents a methodology for efficiently recognizing both isolated and interacting features in a uniform way. The conventional, graph-based recognition method is combined with hint-based feature recognition to recognize and extract alternative interpretations of interacting features. First all isolated (non-intersecting) features are recognized based on a Manufacturing Face Adjacency Graph. Interacting features are then recognized based on the feature's minimal condition subgraph (MCSG) that is used as a feature hint. Unlike Previous hint-based recognition methods, the MCSGs of all features are defined, generated and completed in a uniform way, independent of the feature type. Hints are defined by an Extended Attributed Adjacency Graph, generated by graph decomposition and completed by adding virtual links, corresponding to entities lost by interactions. An efficient algorithm for generating virtual links is developed. A new classification of feature interactions is also presented.

Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses

Abstract: We consider the problem of coding planar graphs by binary strings. Depending on whether O(1)-time queries for adjacency and degree are supported, we present three sets of coding schemes which all take linear time for encoding and decoding. The encoding lengths are significantly shorter than the previously known results in each case.

Head Movement and Adjacency

Abstract: Considerable importance has been attributed to the problem of restricting the theory, but nevertheless certain options that generative transformational grammar provides have remained largely untouched. In the present article, one such issue is broached, viz., that of the choice between substitution and adjunction. The obvious solution of eliminating one of the two options is rejected on empirical grounds, but for the subdomain of head movement it is possible to formulate a theory which will decide whether a particular instance of head movement is a case of adjunction or of substitution. The crucial factor will be seen to be 'adjacency'. The Head Adjacency Principle (HAP) in effect says that any instance of head movement which does not take place under adjacency must be a case of substitution. Evidence for this proposal is presented from a variety of languages and constructions, with particular emphasis on the analysis of the contraction between prepositions and articles, analyzed as D-to-P Raising, in German.

Exploratory spatial data analysis in a geographic information system environment

Abstract: Summary. The paper describes SAGE, a software system that can undertake exploratory spatial data analysis (ESDA) held in the ARC/INFO geographical information system. The aims of ESDA are described and a simple data model is defined associating the elements of 'rough' and 'smooth' with different attribute properties. The distinction is drawn between global and local statistics. SAGE's region building and adjacency matrix modules are described. These allow the user to evaluate the sensitivity of results to the choice of areal partition and measure of interarea adjacency. A range of ESDA techniques are described and examples given. The interaction between the table, map and graph drawing windows in SAGE is illustrated together with the range of data queries that can be implemented based on attribute values and locational criteria. The paper concludes with a brief assessment of the contribution of SAGE to the development of spatial data analysis.

Exploratory Spatial Data Analysis

Abstract: The paper describes SAGE, a software system that can undertake exploratory spatial data analysis (ESDA) held in the ARC/INFO geographical information system. The aims of ESDA are described and a simple data model is defined associating the elements of ‘rough’ and ‘smooth’ with different attribute properties. The distinction is drawn between global and local statistics. SAGE's region building and adjacency matrix modules are described. These allow the user to evaluate the sensitivity of results to the choice of areal partition and measure of interarea adjacency. A range of ESDA techniques are described and examples given. The interaction between the table, map and graph drawing windows in SAGE is illustrated together with the range of data queries that can be implemented based on attribute values and locational criteria. The paper concludes with a brief assessment of the contribution of SAGE to the development of spatial data analysis.

Extension of Edge Connectivity Index. Relationships to Line Graph Indices and QSPR Applications

Abstract: The concept of edge connectivity index is extended to a series of indices based on adjacency between edges in various fragments of the molecular graph. The analogous concept of vertex adjacency indices of the line graph of the molecular graph is also introduced. Some mathematical relations between both series of indices are found, showing that line-graph-based connectivity indices are linear combinations of edge-based descriptors. The study of eight representative physical properties of alkanes was used to compare the ability of both series of indices to produce significant quantitative structure−property relationship (QSPR) models.

Central Limit Theorem for the Adjacency Operators on the Infinite Symmetric Group

Abstract: An adjacency operator on a group is a formal sum of (left) regular representations over a conjugacy class. For such adjacency operators on the infinite symmetric group which are parametrized by the Young diagrams, we discuss the correlation of their powers with respect to the vacuum vector state. We compute exactly the correlation function under suitable normalization and through the infinite volume limit. This approach is viewed as a central limit theorem in quantum probability, where the operators are interpreted as random variables via spectral decomposition. In [K], Kerov showed the corresponding result for one-row Young diagrams. Our formula provides an extension of Kerov's theorem to the case of arbitrary Young diagrams.

Relational histograms for shape indexing

Abstract: This paper is concerned with the retrieval of images from large databases based on their shape similarity to a query image. Our approach is based on two dimensional histograms that encode both the local and global geometric properties of the shapes. The pairwise attributes are the directed segment relative angle and directed relative position. The novelty of the proposed approach is to simultaneously use the relational and structural constraints, derived from an adjacency graph, to gate histogram contributions. We investigate the retrieval capabilities of the method for various queries. We also investigate the robustness of the method to segmentation errors. We conclude that a relational histogram of pairwise segment attributes presents a very efficient way of indexing into large databases. The optimal configuration is obtained when the local features are constructed from six neighbouring segments pairs. Moreover, a sensitivity analysis reveals that segmentation errors do not affect the retrieval performances.

Simplicity surfaces: a new definition of surfaces in Z3

Abstract: In this paper, we introduce a new motion of surfaces in Z3, called simplicity surfaces. In the continuous space, a surface is characterized by the fast that the neighborhood of each point of the surface is homomorphic to an Euclidean disc. The chosen approach consists in characterizing a surface in Z3 by the condition that the neighborhood of any point constitutes a simple closed curve. The major problem is than, if we consider only the usual adjacency relations, this condition is not satisfied even for the simplest surfaces, e.g. digital planes. We thus have to consider another relation. We use a relation for points in Z3 which is based on the notion of homotopy. This allows to define a surface as a connected set of points in which the neighborhood of each point constitutes a simples closed curve for this relation; such a surface is called a simplicity surface. We give two different local characterizations of simplicity surfaces. We then show that a simplicity surface may also be seen as a combinatorial manifold, that is, a set of faces which are linked by an adjacency relation. Furthermore, we show that the main existing notions of surfaces, for the 6- and the 26- adjacency, are also simplicity surfaces.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Representation of 3-D elevation in terrain databases using hierarchical triangulated irregular networks: a comparative analysis

Abstract: 3-D terrain representation plays an important role in a number of terrain database applications. Hierarchical Triangulated Irregular Networks (TINs) provide a variable-resolution terrain representation that is based on a nested triangulation of the terrain. This paper compares and analyzes existing hierarchical triangulation techniques. The comparative analysis takes into account how aesthetically appealing and accurate the resulting terrain representation is. Parameters, such as adjacency, slivers, and streaks, are used to provide a measure on how aesthetically appealing the terrain representation is. Slivers occur when the triangulation produces thin and slivery triangles. Streaks appear when there are too many triangulations done at a given vertex. Simple mathematical expressions are derived for these parameters, thereby providing a fairer and a more easily duplicated comparison. In addition to meeting the adjacency requirement, an aesthetically pleasant hierarchical TINs generation algorithm is expect...

Acoustic modeling system and method using pre-computed data structures for beam tracing and path generation

Abstract: A system and method for acoustic modeling partitions an input 3D spatial model into convex cells, and constructs a cell adjacency data structure representing the neighbor relationships between adjacent cells. For each sound source located in the spatial environment, convex pyramidal beams are traced through the input spatial model via recursive depth-first traversal of the cell-adjacency graph. During beam tracing, a beam tree data structure is constructed to encode propagation paths, which may include specular reflection, transmission, diffuse reflection, and diffraction events, from the source location to regions of the input spatial model. The beam tree data structure is then accessed for real-time computation and auralization of propagation paths to an arbitrary receiver location.

Rectangle-visibility Layouts of Unions and Products of Trees

Abstract: The paper considers representations of unions and products of trees as rectangle-visibility graphs (abbreviated RVGs), ie, graphs whose vertices are rectangles in the plane, with adjacency determined by horizontal and vertical visibility Our main results are that the union of any tree (or forest) with a depth-1 tree is an RVG, and that the union of two depth-2 trees and the union of a depth-3 tree with a matching are subgraphs of RVGs We also show that the cartesian product of two forests is an RVG

Simple and Efficient Graph Compression Schemes for Dense and Complement Graphs

Abstract: We present two graph compression schemes for solving problems on dense graphs and complement graphs. They compress a graph or its complement graph into two kinds of succinct representations based on adjacency intervals and adjacency integers, respectively. These two schemes complement each other for different ranges of density. Using these schemes, we develop optimal or near optimal algorithms for fundamental graph problems. In contrast to previous graph compression schemes, ours are simple and efficient for practical applications.

Method and apparatus for providing continuous level of detail

Abstract: A method and apparatus that provides for off-line generation of, and run-time evaluation for, continuous LODs. The off-line multiresolution generation process is modified and constrained such that a progressive mesh representation for continuous LODs is created that allows properly designed run-time topological data structures to be overloaded to support both LOD construction and optimized rendering. More specifically, the offline generation process initially preprocesses the mesh to generate a triangle-fan covering composed of only complete cycles. The multiresolution generation process is then constrained to maintain this complete cycle covering for every interim mesh. For run-time evaluation, a topological adjacency representation is used that can serve dual uses. This supportive run-time representation is partitioned so as to allow efficient access by the renderer to the subset of the adjacency information that is the fan covering. The multiresolution representation can be generated so as to allow discontinuities to be rendered at some cost to rendering performance.

Compact Implicit Representation of Graphs

Abstract: How to represent a graph in memory is a fundamental data structuring problem. In the usual representations, a graph is stored by representing explicitly all vertices and all edges. The names (labels) assigned to vertices are used only to encode the edges and betray nothing about the structure of the graph itself and hence are a “waste” of space. In this context, we present a general framework for labeling any graph so that adjacency between any two given vertices can be tested in constant time. The labeling schema assigns to each vertex x of a general graph a O(δ(x)log3n) bit label, where n is the number of vertices and δ(x) is x’s degree. The adjacency test can be performed in 5 steps and the schema can be computed in polynomial time. This representation strictly contrasts with usual representations, i.e. adjacency matrix and adjacency list representations, which require O(nlog n) bit label per vertex and constant time adjacency test, and O(δ(x)log n) bit label per vertex and O(logδ (x)) steps to test adjacency, respectively. Additionally, the labeling schema is implicit, that is: no pointers are used.

NP-Completeness of Non-Adjacency Relations on Some 0-1 Polytopes

Abstract: In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.

On boolean topological methods of structural analysis

Abstract: The properties of Boolean methods of structural analysis are used to analyze the intern structure of linear or non linear models. Here they are studied on the particular example of qualitative methods of input-output analysis. First, it is shown that these methods generate informational problems like biases when working in money terms instead of percentages, losses of information, increasing of computation time, and so on. Second, considering three ways to do structural analysis, analysis from the inverse matrix, from the direct matrix and from layers (intermediate flow matrices), these methods induce topological problems; the adjacency of the adjacency cannot be defined from the inverse matrix; the binary relation of influence may be non transitive from the direct matrix, with poorer results than with quantitative methods; for layers - based methods, the information carried out by layers is trivial.

Graph, graph spectra and partitioning algorithms in a geodetic network structural analysis and adjustment

Abstract: Graph theory and its algorithms have been applied in geodesy, viz, structural analysis of networks, and sparse matrix technique in geodetic network adjustment. Fundamental in these applications is the representation of the geodetic network as a graph. Adjacency matrix and the spectra of the Laplacian matrix are shown to have useful properties for both structural analysis and partitioning of a geodetic network. Algorithms for the construction of adjacency matrix, structural analysis, and partitioning of a geodetic network are presented.

Bellman Functions on Trees for Segmentation, Generalized Smoothing, Matching Multi-Alignment in Massive Data Sets

Abstract: A massive data set is considered as a set of experimentally acquired values of a number of variables each of which is associated with the respective node of an undirected adjacency graph that presets the fixed structure of the data set. The class of data analysis problems under consideration is outlined by the assumption that the ultimate aim of processing can be represented as a transformation of the original data array into a secondary array of the same structure but with node variables of, generally speaking, different nature, i.e. different ranges. Such a generalized problem is set as the formal problem of optimization (minimization or maximization) of a real-valued objective function of all the node variables. The objective function is assumed to consist of additive constituents of one or two arguments, respectively, node and edge functions. The former of them carry the data-dependent information on the sought-for values of the secondary variables, whereas the latter ones are meant to express the a priori model constraints. For the case when the graph of the pair-wise adjacency of the data set elements has the form of a tree, an effective global optimization procedure is proposed which is based on a recurrent decomposition of the initial optimization problem over all the node variables into a succession of partial problems each of which consists in optimization of an intervening function of only one variable like Bellman functions in the classical dynamic programming. Two kinds of numerical realization of the basic optimization procedure are considered on the basis of parametric representation of the Bellman functions, respectively, for discretely defined and quadratic node and edge functions. The proposed theoretical approach to the analysis of massive data sets is illustrated with its applications to the problems of segmentation, smoothing, fine texture analysis and matching of visual images and geophysical explorative data, as well as to the problem of multi-alignment of long molecular sequences.

A unified approach to topology generation and optimal sizing of floorplans

Abstract: Existing algorithms for floorplan topology generation by rectangular dualization usually do not consider sizing issues. In this paper, given a rectangularly dualizable adjacency graph and a set of aspect ratios of the modules, a topology which is likely to yield an optimally sized floorplan, is produced first in a top-down fashion by an AI-based search technique with novel heuristic estimates based on size parameters. It is shown that for any rectangular graph, there exists a feasible topology using only either straight or Z-cutlines recursively within a bounding rectangle. The significance of this result is four-fold: (1) considerable acceleration of the heuristic search, (2) topology generation with minimal number of nonslice cores, (3) guaranteed safe routing order without addition of pseudo modules, and (4) design of an efficient bottom-up heuristic for optimal sizing. Experimental results show that this integrated method elegantly solves floorplan optimization problem for general including inherently nonslicible adjacency graphs.

Alignment and Adjacency in Optimality Theory: evidence from Warlpiri and Arrernte

Abstract: The goal of this thesis is to explore alignment and adjacency of constituents in the framework of Optimality Theory. Under the notion of alignment, certain categories, prosodic and morphological, are required to correspond to certain other categories, prosodic or morphological. The alignment of categories is achieved through the operation of constraints which evaluate the well formedness of outputs. The constraints on the alignment of categories and the ranking of these constraints are examined with emphasis on two Australian languages, Warlpiri and Arrernte. The aim is to provide an adequate account in the theory of Optimality of the processes of stress, reduplication and vowel harmony evident in the data. The thesis expands on the range of edges for the alignment of feet. Foot alignment is developed to account for the fact that the edges of intonational phrases, morphemes, and specific morphemes, as well as phonologically specific syllables, play an active role in determining the location of feet. An additional finding is that the location of feet can also be determined by adjacency, resolving conflict between morphological alignment, and ensuring rhythmic harmony. Requirements on adjacency are further supported to account for segmental harmony, where harmony provides evidence for the simultaneous action of segmental and prosodic processes. The analysis provides a unified account of binary and ternary rhythm recommending modifications to alignment of certain categories, thereby laying the groundwork to deal with variation. The account of variation involves relaxing certain constraints. In addition, the notion of rhythm is expanded to account for onset sensitivity to stress, with evidence of this sensitivity found in reduplication and allomorphy. The interaction of prosodic categories with each other and with morphological categories can be directly captured in OT, providing a unified and coherent account of phenomena, some of which were previously seen as exceptions and therefore, unrelated and arbitrary.