Showing papers on "Adjacency list published in 1981"

Connected Component Labeling Using Quadtrees

Abstract: : An algorithm is presented for labeling the connected components of an image represented by a quadtree. The algorithm proceeds by exploring all possible adjacencies for each node once and only once. Once this is done, any equivalences generated by the adjacency labeling phase are propagated. Analysis of the algorithm reveals that its worst case average execution time is bounded by a quantity proportional to the product of the log of the region's diameter and the number of blocks comprising the area connected by the components.

Representation of Three-Dimensional Digital Images

Abstract: Three-dimensional digital images are encountered m a variety of problems, including computed tomography, biological modeling, space planning, and computer vision. A wide spectrum of data structures are available for the computer representation of such images. This paper is a tutorial survey of three-dimensmnal spatial-data representation methods emphasizing techniques that apply to cellular (or voxel-based) images. We attempt to unify data structures for representing interior, surface, and structural information of objects in such images by companng their relative efficmncy. The derivation of high-level representatmns from serial sectmn images is also discussed The representations include topological representations (Euler characteristic and adjacency trees), geometrical representatmns {borders, medial axes, and features), and spatial organization representations {generalized cyhnders and skeletons).

Paley graphs satisfy all first‐order adjacency axioms

Abstract: A graph satisfies Axiom n if, for any sequence of 2n of its points, there is another point adjacent to the first n and not to any of the last n. We show that, for each n, all sufficiently large Paley graphs satisfy Axiom n. From this we conclude at once that several properties of graphs are not first order, including self-complementarity and regularity.

Algorithms for the geometry of semi-algebraic sets

Abstract: Let A be a set of polynomials in r variables with integer coefficients. An A-invariant cylindrical algebraic decomposition (cad) of r-dimensional Euclidean space (G. Collins, Lect. Notes Comp. Sci., 33, Springer-Verlag, 1975, pp 134-183) is a certain cellular decomposition of r-space, such that each cell is a semi-algebraic set, the polynomials of A are sign-invariant on each cell, and the cells are arranged into cylinders. The cad algorithm given by Collins provides, among other applications, the fastest known decision procedure for real closed fields, a cellular decomposition algorithm for semi-algebraic sets, and a method of solving nonlinear (polynomial) optimization problems exactly. The time-consuming calculations with real algebraic numbers required by the algorithm have been an obstacle to its implementation and use. The major contribution of this thesis is a new version of the cad algorithm for r (LESSTHEQ) 3, in which one works with maximal connected A-invariant collections of cells, in such a way as to often avoid the most time-consuming algebraic number calculations. Essential to this new cad algorithm is an algorithm we present for determination of adjacenies among the cells of a cad. Computer programs for the cad and adjacency algorithms have been written, providing the first complete implementation of a cad algorithm. Empirical data obtained from application of these programs are presented and analyzed.

Contour filling in raster graphics

Abstract: The paper discusses algorithms for filling contours in raster graphics. Its major feature is the use of the line adjacency graph for the contour in order to fill correctly nonconvex and multiply connected regions, while starting from a “seed.” Because the same graph is used for a “parity check” filling algorithm, the two types of algorithms can be combined into one. This combination is useful for either finding a seed through a parity check, or for resolving ambiguities in parity on the basis of connectivity.

Contour filling in raster graphics

Abstract: The paper discusses algorithms for filling contours in raster graphics. Its major feature is the use of the line adjacency graph for the contour in order to fill correctly nonconvex and multiply co...

Characterizations of adjacency of faces of polyhedra

Abstract: We generalize the classical concept of adjacency of vertices of a polytope to adjacency of arbitrary faces of a polyhedron. There are three standard ways to describe a polyhedron P, namely, P is given as the intersection of finitely many halfspaces, i.e., P=P(A,b)={x|Ax≤b}, as the convex and conical hull of finitely many vectors, i.e. P=conv(V)+cone(E), or P is given by its face lattice Open image in new window . The adjacency relation of faces is characterized by means of all these three descriptions of a polyhedron. Our main tools in case of the descriptions P=P(A,b) resp. P=conv(V)+cone(E) are “good” characterizations of the equality set and extreme set of a face, respectively. These “good” characterizations enable us to present polynomial algorithms to check adjacency of faces. As a by-product we also obtain polynomial algorithms to make an inequality system Ax≤b nonredundant and to find a minimal generating system (basis) of a polyhedron. All these algorithms are based on the ellipsoid method which checks emptiness resp. nonemptiness of polyhedra in polynomial time.

Combinatorics and graph theory : proceedings of the symposium held at the Indian Statistical Institute, Calcutta, February 25-29, 1980

Abstract: Diperfect Graphs.- Some new problems and results in Graph Theory and other branches of Combinatorial Mathematics.- A form invariant multivariable polynomial representation of graphs.- Some combinatorial applications of the new linear programming algorithm.- In search of a complete invariant for graphs.- Affine triple systems.- Tables of two-graphs.- Designs, adjacency multigraphs and embeddings: A survey.- On the adjugate of a symmetrical balanced incomplete block design with ?=1.- Characterization of potentially connected integer-pair sequences.- Construction and combinatorial properties of orthogonal arrays with variable number of symbols in rows.- Construction of group divisible rotatable designs.- Some path-length properties of graphs and digraphs.- 2-2 Perfect graphic degree sequences.- Characterization of forcibly outerplanar graphic sequences.- Characterization of potentially self-complementary, self-converse degree-pair sequences for digraphs.- Set-reconstruction of chain sizes in a class of finite topologies.- Characterization of forcibly bipartite self-complementary bipartitioned sequences.- A graph theoretical recurrence formula for computing the characteristic polynomial of a matrix.- A note concerning Acharya's conjecture on a spectral measure of structural balance in a social system.- On permutation-generating strings and rosaries.- Enumeration of labelled digraphs and hypergraphs.- Analysis of a spanning tree enumeration algorithm.- Binding number, cycles and complete graphs.- A class of counterexamples to a conjecture on diameter critical graphs.- Reconstruction of a pair of connected graphs from their line-concatenations.- On domination related concepts in Graph Theory.- The local central limit theorem for Stirling numbers of the second kind and an estimate for bell numbers.- A family of hypo-hamiltonian generalized prisms.- Graphical cyclic permutation groups.- Orthogonal main effect plans with variable number of levels for factors.- On molecular and atomic matroids.- New inequalities for the parameters of an association scheme.- On the (4-3)-regular subgraph conjecture.- Enumeration of Latin rectangles via SDR's.- Nearly line regular graphs and their reconstruction.- On reconstructing separable digraphs.- Degree sequences of cacti.- A survey of the theory of potentially P-graphic and forcibly P-graphic degree sequences.- Towards a theory of forcibly hereditary P-graphic sequences.- The minimal forbidden subgraphs for generalized line-graphs.- Spectral characterization of the line graph of K ? n .- Balanced arrays from association schemes and some related results.- Some further combinatorial and constructional aspects of generalized Youden designs.- Maximum degree among vertices of a non-Hamiltonian homogeneously traceable graph.

Characterization of $(r,\,s)$-adjacency graphs of complexes

Abstract: ABSTRAcr. The (r, s)-adjacency graph of a simplicial complex K has been defined as the graph whose nodes are the r-cells of K with adjacency whenever there is incidence with a common s-cell. The (r, s)-adjacency graphs for r > s have been characterized by graph coverings by Dewdney and Harary generalizing the result of Krausz for line-graphs (r = 1, s = 0). We now complete the characterization by handling the case r < s.

Average Case Analysis of an Adjacency Map Searching Technique.

Abstract: : The adjacency map is a data structure (a tree) used to solve the following problem: given a set of parallel segments in the plane and a point p, find the segments closest to p among those intersected by the straight line through p, perpendicular to the common direction of the segments. The search is performed in the repetitive mode, so that preprocessing is convenient. The problem considered is a particular case of planar point location for which algorithms are known (Lipton-Tarjan, Kirkpatrick), which make use of data structures constructed in time 0(nlogn), searched in time 0(logn), and stored in space 0(n). Though asymptotically optimal, the previous algorithms are not very practical. More practical algorithms have been proposed (Preparata, Preparata-Lipski), which use 0(nlogn) space. In this thesis a modification of these algorithm is presented for the adjacency map, and the worst case analysis is performed. The technique is easily extensible to general planar graphs. It is conjectured that, under reasonable assumptions on the input distribution, the new algorithm takes expected linear storage. (Author)