Showing papers on "Adjacency list published in 1991"

Visualization of structural information: automatic drawing of compound digraphs

Abstract: An automatic method for drawing compound digraphs that contain both inclusion edges and adjacency edges are presented. In the method vertices are drawn as rectangles (areas for texts, images, etc.), inclusion edges by the geometric inclusion among the rectangles, and adjacency edges by arrows connecting them. Readability elements such as drawing conventions and rules are identified, and a heuristic algorithm to generate readable diagrams is developed. Several applications are shown to demonstrate the effectiveness of the algorithm. The utilization of curves to improve the quality of diagrams is investigated. A possible set of command primitives for progressively organizing structures within this graph formalism is discussed. The computational time for the applications shows that the algorithm achieves satisfactory performance. >

Hierarchical image analysis using irregular tessellations

Abstract: A novel multiresolution image analysis technique based on hierarchies of irregular tessellations generated in parallel by independent stochastic processes is presented. Like traditional image pyramids these hierarchies are constructed in a number of steps on the order of log(image-size) steps. However, the structure of a hierarchy is adapted to the image content and artifacts of rigid resolution reduction are avoided. Two applications of these techniques are presented: connected component analysis of labeled images and segmentation of gray level images. In labeled images, every connected component is reduced to a separate root, with the adjacency relations among the components also extracted. In gray level images the output is a segmentation of the image into a small number of classes as well as the adjacency graph of the classes. >

A new method for the characterization of topographic surfaces

Abstract: A method is described for the extraction of morphological information from a terrain approximated by a Delaunay triangulation, in order to find a combinatorial simpler surface description while maintaining its basic features. Characteristic regions (i.e., regions with concave, convex, planar or saddle shape) are considered the basic descriptive elements of the surface morphology, and are defined by taking into account the type of adjacency between triangles. Adjacencies between regions define the surface characteristic lines, which are classified as ridges, ravines or generic creases, and characteristic points, which are classified as maxima, minima or saddle points. A graph-like data structure is constructed on these shape features, called the Characteristic Region Configuration Graph, which represents die surface in an effective and concise way.

On using the adjacency matrix power method for perception of symmetry and for isomorphism testing of highly intricate graphs

Abstract: A modification of the adjacency matrix power method described recently for the perception of symmetry in graphs is introduced, which expands the limits of the method far beyond the realm of chemically interesting graphs The procedure finds the automorphism partition even for intricate graphs without performing a tree search The calculation effort increases with the problem size polynomially for all tested cases, including strongly regular graphs, two-level regular graphs, and graphs corresponding to balanced incomplete block designs (BIBD) An equally powerful computer program for testing isomorphism of graphs based on the adjacency matrix power method is introduced

Map representations and coding-based priors for segmentation

Abstract: The Bayesian segmentation model developed is motivated by consideration of the information needed for higher-level visual processing. A segmentation is regarded as a collection of parameters defining an image-valued stochastic process by separating topological (adjacency) and metric (shape) properties of the subdivision and intensity properties of each region. The prior selection is structured accordingly. The novel part of the representation, the subdivision topology, is assigned a prior by universal coding arguments, using the minimum description-length philosophy that the best segmentation allows the most efficient representation of visual data. >

The shortest path problem in the plane with obstacles: a graph modeling approach to producing finite search lists of homotopy classes

Abstract: : The problem of finding the shortest path between two points in a plane containing obstacles is considered. The set of such paths is uncountably infinite, making an exhaustive search impossible. This difficulty is overcome by reducing the size of the search space. The search is first restricted to a countably infinite set by focusing attention on the set of homotopy classes. By applying simple optimality principles, a finite list of such classes is obtained whose union contains the shortest path. This process of simplification is accomplished by modeling the topology of the region with a graph. Optimality principles come into play during a graph traversal which is used to produce the finite search list. In addition, a computational investigation of two methods by which homotopy classes can be named is discussed, and properties of the graph models are investigated. The thesis of CPT Andre M. Cuerington, U.S. Army, calculates the actual shortest path using the search list produced here.

Topological organic chemistry. 3.: graph theory, binary and decimal adjacency matrices and topological indices of Alkanes

Abstract: Adjacency matrices are used as a source of topological indices of alkanes by transformation from the binary to the decimal number system. The data are based upon a canonical numbering system of the graphs

Extracting adjacency relationships from a modular boundary model

Abstract: Modular boundary models are a class of object representations that describe a solid object as a collection of face-abutting components. The face-to-face relationships between components are described in the form of a graph, called the connection graph. The paper addresses the problem of extracting adjacency information from a description of a solid object in terms of a modular boundary model, the FFC model. The encoding structure of the connection graph in such a model is described, and a set of structure-accessing algorithms for retrieving the adjacency relationships from the resulting data structure is defined. Finally, an extension to the connection graph to support instances is briefly presented, and the problems related to the development of adjacency-finding algorithms for such a structure are discussed.

A layered network for the correspondence of 3D objects

Abstract: A computational approach for solving the correspondence problem between different views of objects in range images is presented. This is modeled as a layered constraint satisfaction network which can be implemented on a parallel analog neural network. In this approach, each view of an object is represented by an attributed graph with nodes as surfaces and their bounding vertices, and links as relations between adjacent surfaces. The matching strategy is a two-step process. Each step is formulated with a constraint satisfaction network, and implemented on a Hopfield network. At each level, a set of local, adjacency and global constraints is specified, and an appropriate energy function to be minimized is defined. At the first level of this hierarchy, surface patches are matched and clusters of rotation transformations are hypothesized. At the second level, the computed rotation transformation is applied to the corresponding vertices, and the translation vector is computed. >

Parallel breadth-first and breadth-depth traversals of general trees

Abstract: Two adaptive, level-order tree traversal algorithms are proposed for an exclusive-read and exclusive-write (EREW), parallel random access machine (PRAM) model of computation. Our breadth-first traversal algorithm for a general tree with n nodes achieves O((n/p)*log n /log(n/p)) time complexity using p processors on the EREW model, and hence it attains optimal speedup for p ≤ n1 − e, where 0 < e ≤ 1. This algorithm performs better (in terms of processor-time product) than an existing algorithm [12] which has O(k log n) time complexity using O(n1 + 1/k) processors on a concurrent-read and exclusive-write (CREW), PRAM model. The proposed breadth-depth algorithm for traversing a general tree requires O(n/p + log n) time on the EREW model, and thus it achieves optimal speedup for p ≤ n/log n. This algorithm provides a significant improvement over an existing parallel breadth-depth algorithm [4] which requires O(log n) time with O(n2) processors on CREW model. Our breadth-first traversal algorithm uses an Euler tour technique [20], and a list construction technique which is similar to the one used in [18] for solving the adjacency list construction problem for graphs. The breadth-depth traversal algorithm, on the other hand, is based on a special characterization which enables the reduction of this problem into a variety of list ranking problems.

Graph theoretic approach to segmentation of MR images

Abstract: A novel graph theoretic approach to image segmentation is presented, and its application to tissue segmentation in MR images of the human brain is demonstrated. An undirected adjacency graph G is used to represent the image with each vertex of G corresponding to a homogeneous component of the image. Each component may be a single pixel or a connected region which, under a suitable criterion, is homogeneous. All pairs of nodes corresponding to spatially connected pixels or regions in the image are linked by arcs in G. A flow capacity, assigned to each arc, is chosen to reflect the probability that the pair of linked vertices belong to the same region or tissue type. The segmentation is achieved through clustering vertices in G by removing arcs of G to form mutually exclusive subgraphs. The subgraphs formed by the clustering algorithm are optimal in the sense that the largest inter-subgraph maximum flow is minimized. Each of the resulting subgraphs then represents a homogeneous region of the image. Using a suitable choice of the arc capacity function, this approach can be used to segment the image either by searching for statistically homogeneous regions (texture segmentation) or by searching for closed region boundaries (edge detection). A direct implementation of the new segmentation algorithm requires the construction of a flow equivalent spanning tree for G. As the size of the graph G increases, constructing an equivalent tree becomes very inefficient. In order to overcome this problem, an algorithm for hierarchically constructing and partitioning a partially equivalent tree of much reduced size has been developed. This hierarchical algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree of G.

Area optimization for higher order hierarchical floorplans

Abstract: The floorplan area optimization problem is to determine the dimensions of each module when the topology of the floorplan is given. The objective is to minimize the area of the resulting floorplan. An algorithm for general hierarchical floorplans is presented. The shape curves for non-slicing configurations are constructed by operations on the graph representations of the floorplan. The points of a shape curve are determined by simultaneously reducing the length of all longest paths of the vertical adjacency graph, using a minimum cut technique. The algorithm is applicable to hierarchical floorplans of high order and to modules with an infinite set of possible dimensions. >

Binarity and Ternarity in Alutiiq

Abstract: One of the pillars of phonological research has been the desirability of representing phonological processes as being local in application. Locality, as a principle of the grammar, constrains the relation between the trigger and target elements of a phonological process to one of adjacency. Adjacency, within the framework of Autosegmental Phonology and Underspecification theory, consists of two varieties: tier adjacency and structural adjacency (Myers (1987)). Tier adjacency examines linear relations among elements within an isolated tier of the representation (e.g. the tonal tier), while structural adjacency examines these relations mediated through the skeletal core, which organizes and maintains the linear relations between phonemes and their constituent elements. Locality and Adjacency are not, simply the preserve of featural relations and their skeletal core. The core itself, whether viewed as C/V slots, XIX' timing slots, or Root nodes, is organized into the grander structures of the Prosodic Hierarchy (e.g. syllable, Foot, etc.) . The formation of these units is a phonological process and as such subject to the same principles. A portion of the on -going debates in metrical theory has focused on whether metrical structure, in particular Foot structure, is limited to binary constituents. Kager (1989) proposes an extreme Binarism, with all metrical structure initially being limited to binarity. Hayes (1987) and Prince (1990) only commit to a strong preference for binary Feet. Halle & Vergnaud (1987) propose a system allowing binary, ternary, and unbounded Feet. The principle of Locality with its requirement of adjacency argues for a binary -view of metrical structure where the trigger and target of the structure building process are unmetrified elements. The most serious challenge to this view is the existence of languages which employ ternary constituents, e.g. Cayuvava, Chugach Alutiiq. These languages have been cited as evidence in arguing for a theory capable of generating ternary Feet. In a framework designed to maintain strict locality surface ternary constituents must be derived from underlying binary structures. This paper proposes a solution to this problem which relies on the ternary constituent being a complex constituent composed of a binary Foot grouped with an adjacent syllable. This constituent is not a Foot, but rather a Prosodic Word. Generating an iterative ternary Prosodic Word requires a new algorithm for building metrical structure. This algorithm builds metrical constituents in an opportunistic manner. Opportunistic building creates metrical constituents as soon as possible, instead of applying one particular structure building rule across the whole string before the next rule applies.

On mapping Bezier curve and surface subdivision algorithms into a hypercube with geometric adjacency constraint

Abstract: The authors discuss the Bezier curve and surface generation algorithms on a hypercube computer. They show that the computation structures of Bezier curve and surface generation based on subdivision method can be modeled as binomial trees and extended binomial trees respectively. Properties of binomial trees and extended binomial trees are explored and mappings from these tree structures to hypercubes are discussed. As the spatial coherence plays an important role in computer graphics and geometric algorithms, the authors imposed the geometric adjacency on these mappings and proved that there exist adjacency preserving mappings. Moreover, they show that their mappings are optimal with respect to expansion, dilation and congestion. >

Self-organization of non-numeric data sets

Abstract: A topology-preserving map can be constructed by simulated annealing. This map shares some useful properties with those generated by classical self-organization, but it does not require that the input data have numeric values. An application to mail routing is presented, showing that self-organization can be accomplished given only a local adjacency list. A string-matching application shows the extension of the algorithm to cases where a scalar distance between input points is available. The map in the latter application, like a Kohonen map, exhibits local smoothness permitting shortcuts to the nearest-neighbor search. >

The role of the activity adjacency matrix in the critical path method

Abstract: This paper introduces the use of an activity adjacency matrix in the critical path method to avoid the confusion created by converting the project into its network representation, particularly in performing the cost time trade-offs. A set of APL code was developed to illustrate this point.

Performance of parallel spanning tree algorithms on linear arrays of transputers and Unix systems

Abstract: This paper presents empirical performance of parallel algorithms for computing a spanning tree (SPT) and a minimum spanning tree (MST) of connected graphs on the Transputer and Unix systems, where processors are configured as a one-dimensional array. The parallel MST algorithm uses a weight matrix data structure; and three implementations of the SPT algorithm are presented with unordered edge-list, linked adjacency list and adjacency matrix as data structures. The experiments are conducted with a wide range of random graphs, generated for various edge-densities (d) for a given number (n) of vertices. The edge-density is varied between 0.1 and 0.9, and the maximum number of vertices (or edges) considered are 300 (or 40000) and 500 (or 110000) for transputer and Unix systems, respectively. A maximum speed-up of 2.98 is achieved on the transputer network of eight processors, and that for the Unix system is 3.0 with four processors. >

Markov random field based image labeling with parameter estimation by error backpropagation

Abstract: The authors investigate a method of efficiently labeling images using the Markov random field (MRF). The MRF model is defined on the region adjacency graph and the labeling is then optimally determined using simulated annealing. The MRF model parameters are automatically estimated using an error backpropagation network. The proposed method is analyzed through experiments using real natural scene images. >

Efficient parallel algorithms for some integer problems

Abstract: This paper considers parallel solutions to some problems with integers as input. We first discuss the general integer packing problem and propose a parallel algorithm for this problem on exclusive-read exclusivewrite parallel random-access machine (EREW PRAM). Then we present parallel algorithms on EREW PRAM for bucket sort, graph adjacency-list construction, integer element distinctness, integer set problems (including integer set disjointness, union and difference), and integer max gap. We hope that the address table and general integer packing algorithm proposed in this paper will have other applications in parallel algorithm design.

A certain embedding of a planar graph in the plane

Abstract: Analyses the graph embedding problem. The major difficulty in dealing with the problem is that the embedding of a biconnected graph is not unique (the order of vertices in the ordered adjacency list is not unique and the vertex sets constituting face boundaries are not unique) and there can be many ways to embed graphs especially those arising in IC layout. The embedding is a graph model of a layout where some elements and connecting lines should be placed apart on the plane. The author presents an algorithm for obtaining an embedding which satisfies the condition that no two vertices in the given vertex subset U appear on the same face boundary. This algorithm is based on the vertex addition algorithm for planarity testing and uses a data structure called a PQ-tree. >

Geometrical learning in a network of automata

Abstract: G-NET (Geometrical Network) is a three layers neural network based on linear threshold automata which performs classification in a nearest neighbour fashion. Indeed G-NET defines its class-boundaries as the Voronoi tessellation over the training patterns euclidean space. The network is built incrementally together with the dual Delaunay adjacency relations.