Showing papers on "Adjacency list published in 2002"

Succinct Representation of Balanced Parentheses and Static Trees

Abstract: We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree, and a balanced sequence of parentheses. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been considered in similar work. In the case of binary trees, for instance, we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned. The approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time.

Combinatorial Landscapes

Abstract: Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, nearness, distance, or accessibility. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the ``static'' properties of landscapes as well as their influence on the dynamics of adaptation. In this review we focus on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available.

Using manifold structure for partially labelled classification

Abstract: We consider the general problem of utilizing both labeled and unlabeled data to improve classification accuracy. Under the assumption that the data lie on a submanifold in a high dimensional space, we develop an algorithmic framework to classify a partially labeled data set in a principled manner. The central idea of our approach is that classification functions are naturally defined only on the sub-manifold in question rather than the total ambient space. Using the Laplace Beltrami operator one produces a basis for a Hilbert space of square integrable functions on the submanifold. To recover such a basis, only unlabeled examples are required. Once a basis is obtained, training can be performed using the labeled data set. Our algorithm models the manifold using the adjacency graph for the data and approximates the Laplace Beltrami operator by the graph Laplacian. Practical applications to image and text classification are considered.

Eigenspaces for graphs

Abstract: In this paper, we investigate the feasibility of using graph-based descriptions to learn the view structure of 3D objects. The graphs used in our study are constructed from the Delaunay triangulations of corner features. The investigation is divided into two parts. We commence by considering how relational structures can be encoded in a way which can be used to generate parametric eigenspaces. Here we investigate four different relational representations derived from the graphs. The first three of these are vector encodings of the adjacency graph, the weighted adjacency graph, and the point proximity matrix; the fourth representation is the edge weight histogram. We study the eigenspaces which result from these different representations. In addition, we investigate how multidimensional scaling may be used to generate eigenspaces from a set of pairwise distances between graphs.

A RKHS interpolator-based graph matching algorithm

Abstract: We present an algorithm for performing attributed graph matching. This algorithm is derived from a generalized framework for describing functionally expanded interpolators which is based on the theory of reproducing kernel Hilbert spaces (RKHS). The algorithm incorporates a general approach to a wide class of graph matching problems based on attributed graphs, allowing the structure of the graphs to be based on multiple sets of attributes. No assumption is made about the adjacency structure of the graphs to be matched.

The Topological Structures of Membrane Computing

Abstract: In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes. Using an appropriate abstract setting, this technical device enables us to reformulate also the computation within a membrane and proposes a unified view on several computational mechanisms initially inspired by biological processes. These theoretical tools are instantiated in MGS, an experimental programming language handling various types of membrane structures in a homogeneous and uniform syntax.

A scalable, distributed algorithm for efficient task allocation

Abstract: We present a distributed algorithm for task allocation in multi-agent systems for settings in which agents and tasks are geographically dispersed in two-dimensional space. We describe a method that enables agents to determine individually how to move so that they are, as a group, efficiently assigned to tasks. The method comprises two algorithms and is especially useful in environments with very large numbers of agent and task nodes. One algorithm adapts computational geometry techniques to determine adjacency information for the agent nodes given the geographical positions of agents and tasks. This adjacency information is used to determine the visible nodes that are most relevant to an agent's decision making process and to eliminate those that it should not consider. The second algorithm uses local heuristics based solely on an agent's adjacent nodes to determine its course of action. This method yields improved task allocations compared to previous algorithms proposed for similar environments. We also present a modification to the second algorithm that improves performance in environments in which multiple agents are required to complete a single task.

Testing properties of directed graphs: acyclicity and connectivity

Abstract: This article initiates the study of testing properties of directed graphs. In particular, the article considers the most basic property of directed graphs--acyclicity. Because the choice of representation affects the choice of algorithm, the two main representations of graphs are studied. For the adjacency-matrix representation, most appropriate for dense graphs, a testing algorithm is developed that requires query and time complexity of O(1/e2), where e is a distance parameter independent of the size of the graph. The algorithm, which can probe the adjacency matrix of the graph, accepts every graph that is acyclic, and rejects, with probability at least 2/3, every graph whose adjacency matrix should be modified in at least e fraction of its entries so that it becomes acyclic. For the incidence list representation, most appropriate for sparse graphs, an Ω(|V|1/3) lower bound is proved on the number of queries and the time required for testing, where V is the set of vertices in the graph. Along with acyclicity, this article considers the property of strong connectivity. Contrasting upper and lower bounds are proved for the incidence list representation. In particular, if the testing algorithm can query on both incoming and outgoing edges at each vertex, then it is possible to test strong connectivity in O(1/e) time and query complexity. On the other hand, if the testing algorithm only has access to outgoing edges, then Ω(√N) queries are required to test for strong connectivity.

String Edit Distance, Random Walks and Graph Matching

Abstract: This paper shows how the eigenstructure of the adjacency matrix can be used for the purposes of robust graph-matching. We commence from the observation that the leading eigenvector of a transition probability matrix is the steady state of the associated Markov chain. When the transition matrix is the normalised adjacency matrix of a graph, then the leading eigenvector gives the sequence of nodes of the steady state random walk on the graph. We use this property to convert the nodes in a graph into a string where the node-order is given by the sequence of nodes visited in the random walk. We match graphs represented in this way, by finding the sequence of string edit operations which minimise edit distance.

The Medial Axis Transform

Abstract: This chapter focuses on the medial axis transform of shapes with well-defined mathematical boundaries—that is, lines or smooth curves. The medial axis transform is a one-dimensional graph extracted from a planar shape. The chapter reviews many research results concerning its basic mathematical properties and various algorithms for its accurate and efficient computation. The medial axis of a planar shape is the locus of the centers of a set of disks that maximally fit into the shape; and the medial axis transform is the medial axis together with the corresponding radius values. Points on the medial axis—that is, the centers of such disks, are called the medial axis points of the shape, and medial axis transform points are similarly defined. The chapter presents various algorithms for computing the medial axis. It briefly describes the data structure. The basic scheme is that each maximal circle is denoted by a vertex or a node of a graph, and the edges of the graph are formed according to the usual adjacency rule.

Adjacency preserving maps on matrices and operators

Abstract: We characterize injective continuous maps on the space of real or complex rectangular matrices preserving adjacent pairs of matrices. We also extend Hua's fundamental theorem of the geometry of rectangular matrices to the infinite-dimensional case. An application in the theory of local automorphisms is presented.

Modeling of FPGA local/global interconnect resources and derivation of minimal test configurations

Abstract: This paper addresses the issues of automating the derivation of test configurations (TCs) for both local and global interconnect of SRAM-based FPGAs. We model FPGA interconnect and their test requirements using adjacency graphs and obtain the minimal or near minimal TO by solving the graph coloring problem, using a modified greedy algorithm. We apply the proposed modeling and TC derivation method to the Xilinx XC4000 FPGA. A set of minimal TCs was derived automatically. The proposed method is applicable to FPGAs of various interconnect structures and sizes, and supports distinctive test logic.

Star-vertices: a compact representation for planar meshes with adjacency information

Abstract: In this paper we propose a new structure star-vertex, to represent general planar meshes. The basic concept is simple, allowing constant adjacency query time, and scalability (able to trade size for speed), and under specific situations requiring less storage space than others. For simplicity, we use a generic traverse element, which resembles the behavior of oriented edges. We present implementation examples of the proposed structure and comparisons with other mesh representation schemes.

Exploiting color and topological features for region segmentation with recursive fuzzy C-means

Abstract: In this paper we define a novel approach to image segmentation into regions which focuses on both visual and topological cues, namely color similarity, inclusion and spatial adjacency. Many color clustering algorithms have been proposed in the past for skin lesion images but none exploits explicitly the inclusion properties between regions. Our algorithm is based on a recursive version of fuzzy c-means (FCM) clustering algorithm in the 2D color histogram constructed by Principal Component Analysis (PCA) of the color space. The distinctive feature of the proposal is that recursion is guided by evaluation of adjacency and mutual inclusion properties of extracted regions; then, the recursive analysis addresses only included regions or regions with a not-negligible size. This approach allows a coarse-to-fine segmentation which focuses attention on the inner parts of the images, in order to highlight the internal structure of the object depicted in the image. This could be particularly useful in many applications, especially in biomedical image analysis. In this work we apply the technique to segmentation of skin lesions in dermatoscopic images. It could be a suitable support for diagnosis of skin melanoma, since dermatologists are interested in analysis of spatial relations, symmetrical positions and inclusion of regions.

The Euler Number of Discretized Sets — On the Choice of Adjacency in Homogeneous Lattices

Abstract: Two approaches for determining the Euler-Poincare characteristic of a set observed on lattice points are considered in the context of image analysis — the integral geometric and the polyhedral approach. Information about the set is assumed to be available on lattice points only. In order to retain properties of the Euler number and to provide a good approximation of the true Euler number of the original set in the Euclidean space, the appropriate choice of adjacency in the lattice for the set and its background is crucial. Adjacencies are defined using tessellations of the whole space into polyhedrons. In ℝ3, two new 14 adjacencies are introduced additionally to the well known 6 and 26 adjacencies. For the Euler number of a set and its complement, a consistency relation holds. Each of the pairs of adjacencies (14.1, 14.1), (14.2, 14.2), (6, 26), and (26, 6) is shown to be a pair of complementary adjacencies with respect to this relation. That is, the approximations of the Euler numbers are consistent if the set and its background (complement) are equipped with this pair of adjacencies. Furthermore, sufficient conditions for the correctness of the approximations of the Euler number are given. The analysis of selected microstructures and a simulation study illustrate how the estimated Euler number depends on the chosen adjacency. It also shows that there is not a uniquely best pair of adjacencies with respect to the estimation of the Euler number of a set in Euclidean space.

Fibonacci Polynomials and Parity Domination in Grid Graphs

Abstract: A non-empty set of vertices is called an even dominating set if each vertex in the graph is adjacent to an even number of vertices in the set (adjacency is reflexive). In this paper, the Fibonacci polynomials are studied over GF(2) with particular emphasis on their divisibility properties and their relation to the existence of even dominating sets in grid graphs and properties of a corresponding recurrence.

Process Planning Using Adjacency-Based Feature Extraction

Abstract: The use of attributed adjacency (AA) feature recognition can encapsulate the engineering significance of a part and represent it as a matrix or an arc-node graph. This creates a feature recognition technique that involves scanning a matrix or graph for a combination of zeros (concave relationships/edges) and ones (convex), or smaller arc-node graphs that are predetermined to be features. AA techniques have often suffered problems when dealing with feature interactions, as a feature found must be exactly matched with those stored. This paper presents a modification of the AA matrix and employs a new concept for identifying features and the application in developing software for process planning. A unique feature taxonomy is described, which when combined with the new feature identification system creates a feature recognition and extraction system that includes curved surfaces and eliminates the need for separating interacting primitive features. The new system takes its input from neutral STEP files and produces a list of features with complete information for process planning.

System and method for providing a link state database (LSDB) snapshot for neighbor synchronization

Abstract: A method and apparatus resynchronizes a link state database (LSDB) of router with the LSDB of a neighboring router (“neighbor”) while maintaining an existing adjacency with the neighbor in a computer network. An out-of-band resynchronization process executes on the routers to essentially maintain the existing adjacency between the router and neighbor, rather than resetting that adjacency as defined by a conventional resynchronization approach. By keeping the adjacency “up” from the perspective of a routing protocol, such as the Open Shortest Path First routing protocol, the adjacency can be used for continued data traffic to and from the router.

A visualization model based on adjacency data

Abstract: In this paper, we describe a model whose focus is on data visualization. We assume the data are provided in adjacency format, as is frequently the case in practice. As an example, individuals who buy item a are likely to buy or consider buying items b, c, and d, also. We present a simple technique for obtaining distance measures between data points. Armed with the resulting distance matrix, we show how Sammon maps can be used to visualize the data points. An application to the college selection process is discussed in detail.

QSAR for dihydrofolate reductase inhibitors with molecular graph structural descriptors

Abstract: Molecular graph descriptors are used, together with a large diversity of geometric, electrostatic, and quantum indices, to model physical, chemical, or biological properties with quantitative structure–property relationships and quantitative structure–activity relationships. The interest of developing new graph descriptors for organic compounds was stimulated in recent years by their use in virtual screening of combinatorial libraries, database mining, similarity and diversity assessment. Recently, we have extended topological indices by defining a series of molecular graph operators, providing an effective systematization and generalization of these structural descriptors. A graph operator uses a mathematical equation to compute a family of related molecular graph descriptors with different molecular matrices and various sets of parameters for atoms and bonds. In this paper we use structural descriptors computed with molecular graph operators to develop quantitative structure–activity relationships (QSAR) models for the dihydrofolate reductase inhibition with diaminopyrimidines. The molecular descriptors are derived from five molecular matrices, namely adjacency A , distance D , reciprocal distance RD , distance-path D p , and reciprocal distance-path RD p . The QSAR models are obtained by selecting descriptors with a genetic algorithm, and the best models are validated with the leave-one-out cross-validation method. The QSAR models with the highest prediction power are comparable with those obtained with substituent constants and neural networks, but they use a much lower number of parameters.

Alignment using Spectral Clusters

Abstract: This paper describes a hierarchical spectral method for the correspondence matching of point-sets. Conventional spectral methods for correspondence matching are notoriously susceptible to differences in the relational structure of the point-sets under consideration. In this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. We show how the point-clusters associated with the most significant spectral modes can be used to locate correspondences when significant contamination is present. Spectral graph theory is a term applied to a family of techniques that aim to characterise the global structural properties of graphs using the eigenvalues and eigenvectors of the adjacency matrix [1]. Although the subject has found widespread use in a number of areas including structural chemistry and routeing theory, there have been relatively few applications in the computer vision literature. The reason for this is that although elegant, spectral graph representations are notoriously susceptible to the effect of structural error. In other words, spectral graph theory can furnish very efficient methods for characterising exact relational structures, but soon breaks down when there are spurious nodes and edges in the graphs under study. There are several concrete examples in the pattern analysis literature. Umeyama has an eigendecomposition method that recovers the permutation matrix that maximises the correlation or overlap of the adjacency matrices for graphs of the same size [13]. Horaud and Sossa [5] have adopted a purely structural approach to the recognition of linedrawings. Their representation is based on the immanantal polynomials for the Laplacian matrix of the line-connectivity graph. By comparing the coefficients of the polynomials, they are able to index into a large data-base of line-drawings. Shapiro and Brady [11] have developed a method which draws on a representation which uses weighted edges. They commence from a weighted adjacency matrix (or proximity matrix) which is obtained using a Gaussian function of the distances between pairs of points. The eigen-vectors of the adjacency matrix can be viewed as the basis vectors of an orthogonal transformation on the original point identities. In other words, the components of the eigenvectors represent mixing angles for the transformed points. Matching between different point-sets is effected by comparing the pattern of eigenvectors in different images. Finally, a number of authors have used spectral methods to perform pairwise clustering on image data. Shi and Malik [12] use the second eigenvalue to segment grey-scale images by performing an eigen-decomposition on a matrix of pairwise attribute differences. Inoue and Urahama [6] have shown how the sequential extraction of eigen-modes can be used to cluster pairwise

Topological adjacency relations on Z, n

Abstract: For which adjacency relations (i.e., irreflexive symmetric binary relations) on Zn does there exist a topology on Zn such that the -connected sets are exactly the -path-connected subsets of Zn? If such a topology exists then we say that the relation is topological. Let l1 and l, respectively, denote the 4- and the 8-adjacency relations on Z2 and the analogs of these two relations on Zn (for any positive integer n). Consider adjacency relations on Zn such that 1.For x,yZn,xl1yxyxly. 2.For all xZn, the set {x}{y|xy} is l1-path-connected. Among the uncountably many adjacency relations satisfying conditions 1 and 2 above, Eckhardt and Latecki showed that there are (up to isomorphism) just two topological relations on Z2, and essentially showed that there are just four topological relations on Z3. We show in this paper that for any positive integer n there are only finitely many topological adjacency relations on Zn that satisfy conditions 1 and 2, and we relate the problem of finding these relations to the problem of finding all sets of vertices of an n-cube such that no two vertices in the set are the endpoints of an edge of the n-cube. From our main theorems we deduce the above-mentioned results of Latecki and Eckhardt, and also deduce that there are (again, up to isomorphism) exactly 16 topological adjacency relations on Z4 that satisfy conditions 1 and 2.

Automatic service configuration method for synchronous digital transmission system

Abstract: A method for automatic allocating transactions of a synchronous digital transmission system includes following steps. (1) Network units and network topologies within a network are pre processed. The relevant loop mark number and the number of network unit on the network unit allocation list, the loop adjacency list and the case list of the loop cross point are stored to the database on the part of administration of networks. (2) A route selection program, a program for processing port time slot occupation and a processing program for automatic allocating transactions are built on the part of administration of network. (3) The foreground-processing program is built on the network units control part. Only a user needs to establish the quantity and type of transactions and the source networkunit, then the invented system can allocate transactions automatically so as to reduce workload and complexity greatly.

System and method for reconstructing pathways in large genetic networks from genetic perturbations

Abstract: A system and method for reconstructing pathways in large genetic networks from genetic perturbations comprises an analysis method and system that applies a recursive algorithm for determining the path between every gene pair in an arbitrarily large genetic network from large-scale gene perturbation data and reconstructs all direct and indirect regulatory gene interactions in the network. Graph theory mathematics is applied to genetic network reconstruction in the following manner: Genetic perturbation data is used to identify all genes accessible from a perturbed gene to generate an accessibility list for the gene. Graph theory mathematics is applied to the accessibility list and its graph to determine a condensation of the graph as defined by the condensation's accessibility list. Graph theory mathematics is applied to the accessibility list, such as through a recursive algorithm performed on a desktop computer, to obtain an adjacency list for the gene that characterizes a genetic network.

Rapidly Mixing Markov Chains for Dismantleable Constraint Graphs

Abstract: If G = (VG, EG) is an input graph, and H = (VH, EH) a fixed constraint graph, we study the set ? of homomorphisms (or colorings) from VG to VH, i.e., functions that preserve adjacency. Brightwell and Winkler introduced the notion of dismantleable constraint graph to characterize those H whose associated set ? of homomorphisms is, for every G, connected under single vertex recolorings. Given fugacities ?(c) > 0 (c ? VH) our focus is on sampling a coloring &omega ? ? according to the Gibbs distribution, i.e., with probability proportional to ?v?VG ?(?(v)). The Glauber dynamics is a Markov chain on ? which recolors a single vertex at each step, and leaves invariant the Gibbs distribution. We prove that, for each dismantleable H and degree bound ?, there exist positive constant fugacities on VH such that the Glauber dynamics has mixing time O(n2), for all graphs G whose vertex degrees are bounded by ?.