Showing papers on "Adjacency list published in 1986"

Topological Structures for Geometric Modeling

Abstract: Geometric modeling technology for representing three-dimensional objects has progressed from early wireframe representations, through surface representations, to the most recent representation, solid modeling. Each of these forms has many possible representations. The boundary representation technique, where the surfaces, edges, and vertices of objects are represented explicitly, has found particularly wide application. Many of the more sophisticated versions of boundary representations explicitly store topological information about the positional relationships among surfaces, edges, and vertices. This thesis places emphasis on the use of topological information about the shape being modeled to provide a framework for geometric modeling boundary representations and their implementations, while placing little constraint on the actual geometric surface representations used. The major thrusts of the thesis fall into two areas of geometric modeling. First, a theoretical basis for two-manifold solid modeling boundary topology representation is developed. The minimum theoretical and minimum practical topological adjacency information required for the unambiguous topological representation of manifold solid objects is determined. This provides a basis for checking the correctness of existing and proposed representations. The correctness of the winged edge structure is also explored, and several new representations which have advantages over existing techniques are described and their sufficiency verified. Second, a non-two-manifold boundary geometric modeling topology representation is developed which allows the unified and simultaneous representation of wireframe, surface, and solid modeling forms, while featuring a representable range beyond what is achievable in any of the previous modeling forms. In addition to exterior surface features, interior features can be modeled, and non-manifold features can be represented directly. A new data structure, the Radial Edge structure, which provides access to all topological adjacencies in a non-manifold boundary representation, is described and its completeness is verified. A general set of non-manifold topology manipulation operators is also described which is independent of a specific data structure and is useful for insulating higher levels of geometric modeling functionality from the specifics and complexities of underlying data structures. The coordination of geometric and topological information in a geometric modeling system is also discussed.

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.

Natural language processing in information retrieval

Abstract: The role and contributions of natural-language processing in information-retrieval and artificial-intelligence research is examined in the context of large operational information-retrieval systems and services. State-of-the-art information-retrieval systems are found to combine the functional capabilities of the conventional inverted file—Boolean logic—term adjacency approach, commonly employed by commercial search services, with statistical-combinatoric techniques pioneered in experimental information-retrieval research and formal natural-language processing methods and tools borrowed from artificial intelligence. © 1986 John Wiley & Sons, Inc.

The Constraints on Images of Rectangular Polyhedra

Abstract: This paper discusses how polyhedron interpretation techniques are simplified if the objects are rectangular trihedral polyhedra. This restriction enables one to compute the spatial orientation of a given corner and its motion from its image in terms of polar coordinates, Eulerian angles, and quaternions. One can also interpret the shape and the face adjacency from local information only. The necessary constraints are listed, and some examples are given to compare the presented scheme to existing ones. The possible nonuniqueness of the interpretation is also discussed.

Recognizing Outerplanar Graphs in Linear Time

Abstract: This paper describes a linear time algorithm to determine whether an arbitrary graph is outerplanar. The algorithm uses an edge coloring technique and deletes successively vertices of degree less than or equal to two. If the degree of a vertex is two, both neighbors of the vertex are joined by an edge. The algorithm works without splitting the graph into its biconnected components or using bucket sort to give the adjacency lists a special order.

Adjacency in binary matroids

Abstract: We say that two elements e , f of a binary matroid M are ‘adjacent’ if there is no minor of M isomorphic to ℳ( K 4 ) which uses both e and f and in which they correspond to opposite edges. We give a good characterization of when two elements are adjacent. In particular, we show that if M is 4-connected, elements e , f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph. We deduce a theorem about disjoint paths in graphs.

Consistent Operations on a Spatial Data Structure

Abstract: Geometric objects such as polygons, line segments, and points may have manifold relations among each other, i.e., order, adjacency, connectivity, etc., and may be stored in a database. For the design of the spatial data structure and in order to preserve consistency when manipulating the data, we propose a graph grammar approach. All consistent states are described by a structure graph, and the manipulation rules are given by productions where intersection problems as well as topologic properties have to be solved. By appropriately modeling the behavior of geographic data, consistency is preserved at all times. This eliminates the tedious case of recovering a geographic database after an inconsistency has been detected.

A Hierarchical Segmentation Algorithm

Abstract: We present a new segmentation algorithm based upon a region growing technique. An initial segmentation is obtained using a MERGE procedure described by Pavlidis. We then build an adjacency graph of regions pairs.

An Implementation of a State Assignment Heuristic

Abstract: This paper presents the results of developing and integrating a Finite State Machine(FSM) state-assignment tool into the functional design part of the Intel PLA-based synthesis system. The tool developed is an heuristic adjacency-based state assignment program , based on the KISS program [DeMicheli85]. Statistics are presented, relative to the tool, on 28 FSM's. The current state of the functional design tool is described, as is the interface with the new tool. A new abstract mathematical method, which joins the adjacency and partition methods of assigning states is outlined.

BANGALORE: an algorithm for the optimal minimization of programmable logic arrays

Abstract: The paper describes BANGALORE, a minterm based algorithm for the optimal minimization of programmable logic arrays (PLA), The algorithm is a divide and conquer algorithm and is carried out by five procedures. The algorithm is mainly guided by two parameters, the degree of adjacency (DA) and the candidate product term (CPT), which are selectively computed for those minterms that participate in the generation of product terms constituting the optimal solution. The algorithm also handles a multiple output function whose individual functions are cyclic functions. For the implementation of the multiple output function using a PLA, the algorithm produces the C-matrix (AND plane) and the D-matrix (OR plane), where the number of product lines and the cross points are minimal. The algorithm does not generate any superfluous product term or the OFF set of any function. Consequently, the number of computations turn out to be quite minimal. As such, it is likely to be more efficient and faster than many existing logi...

A topological characterization of

Abstract: A large number of skeletonization algorithms for binary images use the method of thinning: successive layers of pixels are deleted from the figure until it becomes one pixel thick. In this paper we analyze the topological properties of the set D of pixels to be deleted from a figure F in order to get a skeleton. We characterize them by the concept of strong k-deletability (k = 4 or 8). For individual pixels, strong k-deletability is equivalent to a more general property that we call k-deletability, which is a well-known connectivity requirement assumed--at least implicitly--in all existing thinning algorithms. We show then that a strongly k-deletable subset D of a figure F can be deleted by a succession of deletions of individual pixels Pl,..., Pt, where each Pl is k-deletable from F\{pjIj< i}. This justifies our definition of strong deletability and shows that any topologically valid skeleton can be obtained by some thinning process. One can find in the literature a large number of algorithms producing skeletons from arbitrary binary images. Most of them use the method of thinning: successive layers of pixels are deleted from the figure until it becomes one pixel thick. In general, the pixels are deleted according to certain criteria based on the configuration of white and black pixels in their 8-neighbourhood. We do not intend to list them; we can give as examples the algorithms of (2) and (8), which are sequential and parallel respectively. The features which must be retained in the skeletonization process are of a 'topological' or 'geometrical' nature (see also (1 )). The 'digital topology' considered here is based on the adjacency relations between pixels and has a different meaning from what one calls 'topology' or 'discrete topology' in mathematics (based on open and closed sets), although some concepts (connectedness, holes, Euler numbers, etc.) can be defined in both. In fact, the topological requirements of skeletonization can be stated in very rigorous terms, while the geometrical requirements are more vague and admit different~mathematical formulations. In this paper we study the topological aspects of the skeletonization process. Although one often claims that the topological requirements of thinning are well

A Surprising Property of Some Regular Polytopes

Abstract: : The Platonic solids and some other polytopes have the property that the adjacency information contained in the skeleton (graph) is enough to determine the polytope completely. In particular, the eigenmatrix of the adjacency matrix corresponding to the second eigenvalue provides the coordinates of the vertices. (Author)

Form Feature Representation in a Structured Boundary Model

Abstract: A relational boundary model of a solid object, based on a structured graph representation is presented, and its application to the description of form features is discussed. In this hierarchical graph structure, called Structured Face Adjacency Graph, the global shape of an object is represented at the highest level of abstraction, while its representation details can be described at lower levels of specification. In the paper, we show how explicit topological form features, grouped into three main categories, namely through holes, protrusions or depressions, and connections, can be represented in this graph model as lower level attributes of the main object shape. We define also two basic transformations on the structured face adjacency graph, termed refinement and abstraction, which allow local modifications of its hierarchical structure, especially useful to reorganize object descriptions during the process planning step.

Optimal rectangle covers for convex rectilinear polygon

Abstract: Optimal Rectangle Covers for Convex Rectilinear Polygons Rectilinear Polygons have all their edges parallel to the x and y axes. The problem of finding a minimum cardinality set of rectilinearly oriented rectangles that cover the area of a rectilinear polygon has applications in image processing, pattern recognition and VLSI, and is of use in solving other problems in computational geometry. Such a set is called an optimal rectangle area cover (ORAC). Associated problems are those of finding an optimal rectangle corner cover (ORCC) or edge cover (OREC) of a rectilinear polygon. A rectilinear polygon is convex in the x (y) direction if any horizontal (vertical) line drawn through the polygon intersects it no more than twice. A semi-convex polygon is convex in either the x or y direction. A convex rectilinear polygon is convex in both x and y directions. Five linear algorithms are presented. The first algorithm finds an ORCC for a convex rectilinear polygon. The remaining algorithms are adaptions of this first method. Algorithm E l finds an OREC for a class of convex rectilinear polygons called irreducible. Algorithm E2 finds an edge cover within one rectangle of optimal for general polygons. Algorithms A1 and A2 find area covers within one rectangle of optimal for irreducible and general polygons. respectively. A method used in the ORCC algorithm finds a maximum matching in a bipartite graph with a rectilinearly convex adjacency matrix in O(IVI) time, providing the ranges of adjacency or the adjacency matrix is given. A similar method can be used to find maximum matchings in bipartite graphs whose adjacency matrices have the consecutive 1's property in O(IVl1oglVI) time providing the ranges of adjacency or the adjacency matrix is given.

Block plan construction from a deltahedron-based adjacency graph

Abstract: : A method for the construction of a rectangular geometric dual from a Deltahedron based maximally planar adjacency graph is given along with its computer implementation. In addition, a method and its computer implementation for the addition of areas to form a block plan is given. Comparisons with output from other computer methods is included. Possible extensions include the construction of a rectangular geometric dual with areas for all maximally planar and adjacency graphs.