Abstract: The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution. We report on experiments on local and global properties of the web graph using two Altavista crawls each with over 200 million pages and 1.5 billion links. Our study indicates that the macroscopic structure of the web is considerably more intricate than suggested by earlier experiments on a smaller scale.

Abstract: The world-wide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scale-free characteristics. We introduce a model that leads to a scale-free network, capturing in a minimal fashion the self-organization processes governing the world-wide web. c 2000 Elsevier Science B.V. All rights reserved. PACS: 84.35.+i; 64.60.Fr; 87.23.Ge

Abstract: This paper proposes a novel approach named AGM to efficiently mine the association rules among the frequently appearing substructures in a given graph data set A graph transaction is represented by an adjacency matrix, and the frequent patterns appearing in the matrices are mined through the extended algorithm of the basket analysis Its performance has been evaluated for the artificial simulation data and the carcinogenesis data of Oxford University and NTP Its high efficiency has been confirmed for the size of a real-world problem

Abstract: We study the problem of finding highly connected subgraphs of undirected and directed graphs. For undirected graphs, the notion of density of a subgraph we use is the average degree of the subgraph. For directed graphs, a corresponding notion of density was introduced recently by Kannan and Vinay. This is designed to quantify highly connectedness of substructures in a sparse directed graph such as the web graph. We study the optimization problems of finding subgraphs maximizing these notions of density for undirected and directed graphs. This paper gives simple greedy approximation algorithms for these optimization problems. We also answer an open question about the complexity of the optimization problem for directed graphs.

Abstract: This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian representations. The authors' previous result that the complex is delta-hyperbolic was hard to apply because the complex is not locally finite; in this paper some tools are developed for overcoming this problem, and a combinatorial mechanism introduced which describes sequences of elementary moves in the graph of markings on a surface. These tools are applied to give a family of quasi-geodesic words in the Mapping Class Group, and a linear bound on the shortest word conjugating two conjugate pseudo-Anosov elements. A basic tool in the analysis is a family of subsurface projections, which are roughly analogous to closest-point projections to horoballs in classical hyperbolic space. These projections have a strong contraction property which makes it possible to tie together the geometry of the complex and that of the (infinite) subcomplexes that arise as links of vertices. The resulting layered structure of the complex is controlled by means of a combinatorial device called a hierarchy of geodesics, which is the central construction of the paper.

Abstract: Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.

Abstract: INTRODUCTION A Systematic Design Methodology Links and Joints Kinematic Chains, Mechanisms, and Machines Kinematics of Mechanisms Planar, Spherical, and Spatial Mechanisms Kinematic Inversions BASIC CONCEPT OF GRAPH THEORY Definitions Tree Planar Graph Spanning Trees and Fundamental Circuits Euler's Equation Topological Characteristics of Planar Graphs Matrix Representation of Graphs Contracted Graphs Dual Graphs STRUCTURAL REPRESENTATIONS OF MECHANISMS Functional Schematic Representation Structural Representation Graph Representation Matrix Representation STRUCTURAL ANALYSIS OF MECHANISMS Correspondence between Mechanisms and Graphs Degrees of Freedom Loop Mobility Criterion Lower and Upper Bounds on the Number of Joints on a Link Link Assortments Partition of Binary Link Chains Structural Isomorphism Permutation Group and Group of Automorphisms Identification of Structural Isomorphism Partially Locked Kinematic Chains ENUMERATION OF GRAPHS OF KINEMATIC CHAINS Enumeration of Contracted Graphs Enumeration of Conventional Graphs Atlas of Graphs of Kinematic Chains CLASSIFICATION OF MECHANISMS Planar Mechanisms Spherical Mechanisms Spatial Mechanisms EPICYCLIC GEAR TRAINS Structural Characteristics Buchsbaum-Freudenstein Method Genetic Graph Approach Parent Bar Linkage Method Mechanism Pseudo Isomorphisms Atlas of Epicyclic Gear Trains Kinematics of Epicyclic Gear Trains AUTOMOTIVE MECHANISMS Variable-Stroke Engine Mechanisms Constant-Velocity Shaft Couplings Automatic Transmission Mechanisms Canonical Graph Representation of EGMs Atlas of Epicyclic Gear Transmission Mechanisms ROBOTIC MECHANISMS Parallel Manipulators Robotic Wrist Mechanisms APPENDICES: A. Solving m Equations in n unknowns B. Atlas of Contracted Graphs C. Atlas of Graphs of Kinematic Chains D. Atlas of Planar Bar Linkages E. Atlas of Spatial One-dof Kinematic Chains F. Atlas of Epicyclic Gear Trains G. Atlas of Epicyclic Gear Transmission Mechanisms NOTE: Introduction at the beginning of Chapters 1,3-9 Summary at the end of Chapters 1-6,8-9

Abstract: The pages and hyperlinks of the World-Wide Web may be viewed as nodes and edges in a directed graph. This graph has about a billion nodes today, several billion links, and appears to grow exponentially with time. There are many reasons—mathematical, sociological, and commercial—for studying the evolution of this graph. We first review a set of algorithms that operate on the Web graph, addressing problems from Web search, automatic community discovery, and classification. We then recall a number of measurements and properties of the Web graph. Noting that traditional random graph models do not explain these observations, we propose a new family of random graph models.

Abstract: This paper describes a new algorithm for flow and context insensitive pointer analysis of C programs. Our studies show that the most common use of pointers in C programs is in passing the addresses of composite objects or updateable values as arguments to procedures. Therefore, we have designed a low-cost algorithm that handles this common case accurately. In terms of both precision and running time, this algorithm lies between Steensgaard's algorithm, which treats assignments bi-directionally using unification, and Andersen's algorithm, which treats assignments directionally using subtyping. Our “one level flow” algorithm uses a restricted form of subtyping to avoid unification of symbols at the top levels of pointer chains in the points-to graph, while using unification elsewhere in the graph. The method scales easily to large programs. For instance, we are able to analyze a 1.4 MLOC (million lines of code) program in two minutes, using less than 200MB of memory. At the same time, the precision of our algorithm is very close to that of Andersen's algorithm. On all of the integer benchmark programs from SPEC95, the one level flow algorithm and Andersen's algorithm produce either identical or essentially identical points-to information. Therefore, we claim that our algorithm provides a method for obtaining precise flow-insensitive points-to information for large C programs.

Abstract: Bayesian networks (BNs) model problems that involve uncertainty. A BN is a directed graph, whose nodes are the uncertain variables and whose edges are the causal or influential links between the variables. Associated with each node is a set of conditional probability functions that model the uncertain relationship between the node and its parents. The benefits of using BNs to model uncertain domains are well known, especially since the recent breakthroughs in algorithms and tools to implement them. However, there have been serious problems for practitioners trying to use BNs to solve realistic problems. This is because, although the tools make it possible to execute large-scale BNs efficiently, there have been no guidelines on building BNs. Specifically, practitioners face two significant barriers. The first barrier is that of specifying the graph structure such that it is a sensible model of the types of reasoning being applied. The second barrier is that of eliciting the conditional probability values. In this paper we concentrate on this first problem. Our solution is based on the notion of generally applicable “building blocks”, called idioms, which serve solution patterns. These can then in turn be combined into larger BNs, using simple combination rules and by exploiting recent ideas on modular and object oriented BNs (OOBNs). This approach, which has been implemented in a BN tool, can be applied in many problem domains. We use examples to illustrate how it has been applied to build large-scale BNs for predicting software safety. In the paper we review related research from the knowledge and software engineering literature. This provides some context to the work and supports our argument that BN knowledge engineers require the same types of processes, methods and strategies enjoyed by systems and software engineers if they are to succeed in producing timely, quality and cost-effective BN decision support solutions.

Abstract: Software change requests are often formulated as requests to modify or to add a specific feature or concept. To implement these changes, the features or concepts must be located in the code. We describe the scenarios of the feature and concept location. The scenarios utilize a computer-assisted search of software dependence graph. Scenarios are demonstrated by a case study of NCSA Mosaic source code.

Abstract: A class of biometrics based upon ear features is introduced for use in the development of passive identification systems. The viability of the proposed biometric is shown both theoretically in terms of the uniqueness and measurability over time of the ear, and in practice through the implementation of a computer vision based system. Each subject's ear is modeled as an adjacency graph built from the Voronoi diagram of its curve segments. We introduce a novel graph matching based algorithm for authentication which takes into account the erroneous curve segments which can occur due to changes (e.g., lighting, shadowing, and occlusion) in the ear image. This class of biometrics is ideal for passive identification because the features are robust and can be reliably extracted from a distance.

Abstract: This paper presents different algorithms, based on a combination of two structures of a graph and of two color image processing methods, in order to segment color images. The structures used in this study are the region adjacency graph and the associated line graph. We see how these structures can enhance segmentation processes such as region growing or watershed transformation. The principal advantage of these structures is that they give more weight to the adjacency relationships between regions than the usual methods. We note, nevertheless, that this advantage leads the adjustment of more parameters than other methods to best refine the result of the segmentation. We show that this adjustment is necessarily image dependent and observer dependent.

Abstract: Alon, Krivelevich, and Sudakov [Random Struct Algorithms 13(3–4) (1998), 457–466.] designed an algorithm based on spectral techniques that almost surely finds a clique of size hidden in an otherwise random graph. We show that a different algorithm, based on the Lovasz theta function, almost surely both finds the hidden clique and certifies its optimality. Our algorithm has an additional advantage of being more robust: it also works in a semirandom hidden clique model, in which an adversary can remove edges from the random portion of the graph. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 195–208, 2000

Abstract: To guarantee typesafe execution, Java and other strongly typed languages require bounds checking of array accesses. Because array-bounds checks may raise exceptions, they block code motion of instructions with side effects, thus preventing many useful code optimizations, such as partial redundancy elimination or instruction scheduling of memory operations. Furthermore, because it is not expressible at bytecode level, the elimination of bounds checks can only be performed at run time, after the bytecode program is loaded. Using existing powerful bounds-check optimizers at run time is not feasible, however, because they are too heavyweight for the dynamic compilation setting.ABCD is a light-weight algorithm for elimination of Array Bounds Checks on Demand. Its design emphasizes simplicity and efficiency. In essence, ABCD works by adding a few edges to the SSA value graph and performing a simple traversal of the graph. Despite its simplicity, ABCD is surprisingly powerful. On our benchmarks, ABCD removes on average 45% of dynamic bound check instructions, sometimes achieving near-ideal optimization. The efficiency of ABCD stems from two factors. First, ABCD works on a sparse representation. As a result, it requires on average fewer than 10 simple analysis steps per bounds check. Second, ABCD is demand-driven. It can be applied to a set of frequently executed (hot) bounds checks, which makes it suitable for the dynamic-compilation setting, in which compile-time cost is constrained but hot statements are known.

Abstract: We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms.The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in O(n2+μ) time, where μ satisfies the equation ω(1, μ, 1) = 1 + 2μ and ω(1, μ, 1) is the exponent of the multiplication of an n × nμ matrix by an nμ × n matrix. Currently, the best available bounds on ω(1, μ, 1), obtained by Coppersmith, imply that μ 0 is an error parameter and W is the largest edge weight in the graph, after the edge weights are scaled so that the smallest non-zero edge weight in the graph is 1. It returns estimates of all the distances in the graph with a stretch of at most 1 + ϵ. Corresponding paths can also be found efficiently.

Abstract: In a knowledge classification system, both the information sources and queries are processed to generate knowledge representation graph structures. The graph structures for both the query and the information sources are then converted to views and displayed to a searcher. By manipulating the graph structure views for each information source, the searcher can examine the source for relevance. A search can be performed by comparing the graph structure of the query to the graph structure of each information source by a graph matching computer algorithm. Information sources are classified by constructing hierarchies of knowledge representations. The simplest construction is obtained by using the knowledge representation of a query as the top of the hierarchy. The structures in the hierarchy are substructures of the query. The hierarchy of structures may also be constructed by using the knowledge representation of the query as the bottom of the hierarchy. Structures in the hierarchy, in this case, are structures that contain the query. The vertices of a graph structure view can be displayed on a computer screen next to the corresponding items, such as words, phrases and visual features, of an information source view. Selecting a vertex in the graph structure causes the selected vertex and vertices adjacent to the selected vertex to be “highlighted.” By selecting a succession of vertices in the graph structure, a searcher can perform knowledge navigation of the information source. By successively selecting items of the information source, a searcher can perform knowledge exploration of the information source.

Abstract: Perceptual organization offers an elegant framework to group low-level features that are likely to come from a single object. We offer a novel strategy to adapt this grouping process to objects in a domain. Given a set of training images of objects in context, the associated learning process decides on the relative importance of the basic salient relationships such as proximity, parallelness, continuity, junctions, and common region toward segregating the objects from the background. The parameters of the grouping process are cast as probabilistic specifications of Bayesian networks that need to be learned. This learning is accomplished using a team of stochastic automata in an N-player cooperative game framework. The grouping process, which is based on graph partitioning is able to form large groups from relationships defined over a small set of primitives and is fast. We statistically demonstrate the robust performance of the grouping and the learning frameworks on a variety of real images. Among the interesting conclusions is the significant role of photometric attributes in grouping and the ability to form large salient groups from a set of local relations, each defined over a small number of primitives.

Abstract: Graphs are a powerful and versatile tool useful in various subfields of science and engineering. In many applications, for example, in pattern recognition and computer vision, it is required to measure the similarity of objects. When graphs are used for the representation of structured objects, then the problem of measuring object similarity turns into the problem of computing the similarity of graphs, which is also known as graph matching. In this paper, similarity measures on graphs and related algorithms are reviewed. Also theoretical work showing various relations between different similarity measures is discussed. Other topics to be addressed include graph clustering and efficient indexing of large databases of graphs.

Abstract: Fingerprint matching is challenging as the matcher has to minimize two competing error rates: the False Accept Rate and the False Reject Rate. We propose a novel, efficient, accurate and distortion-tolerant fingerprint authentication technique based on graph representation. Using the fingerprint minutiae features, a labeled, and weighted graph of minutiae is constructed for both the query fingerprint and the reference fingerprint. In the first phase, we obtain a minimum set of matched node pairs by matching their neighborhood structures. In the second phase, we include more pairs in the match by comparing distances with respect to matched pairs obtained in first phase. An optional third phase, extending the neighborhood around each feature, is entered if we cannot arrive at a decision based on the analysis in first two phases. The proposed algorithm has been tested with excellent results on a large private livescan database obtained with optical scanners.

Abstract: Graph data is an emerging model for representing a variety of database contexts ranging from object-oriented databases to hypertext data. Also many of the recursive queries that arise in relational databases are, in practice, graph traversals. In this paper we present a language for searching graph-like databases. The language permits us to express paths in a graph by means of extended regular expressions. The proposed extension is based on the introduction of constructs which permit us i) to define a partial order on the paths used to search the graph and, consequently, on the answers of queries, and ii) to cut off, nondeterministically, tuples with low priority. We present an algebra for partially ordered relations and an algorithm for the computation of path queries. Finally, we present applications to hypertext databases such as the Web.

Abstract: This paper presents an algorithm which extends the probabilistic roadmap (PRM) framework to handle manipulation planning. This is done by using a two level approach, a PRM of PRMs. The first level builds a manipulation graph, whose nodes represent stable placements of the manipulated objects while the edges represent transfer and transit actions. The actual motion planning for the transfer and transit paths is done by PRM planners at the second level. The approach is made possible by the introduction of a new kind of roadmap, called the fuzzy roadmap. The fuzzy roadmap contains edges which are not verified by a local planner during construction. Instead, each edge is assigned a number which represents the probability that it is feasible. Later, if the edge is part of a solution path, the edge is checked for collisions. The overall effect is that our roadmaps evolve iteratively until they contain a solution. The use of fuzzy roadmaps in both levels of our manipulation planner offers many advantages. At the first level, a fuzzy roadmap represents the manipulation graph and addresses the problem of having probabilistically complete planners at the second level. At the second level, fuzzy roadmaps drastically reduce the number of collision checks. The paper contains experimental results demonstrating the feasibility and efficiency of our scheme.

Abstract: The selection of measurements is one of the most important problems in the design of process instrumentation. This paper deals with the design of sensor networks such that the observability of the variables, which are necessary for the process control, remains satisfied in the presence of sensor failures. Pseudo-minimal and minimal sensor sets are organized into an oriented graph which contains all the possible reconfiguration paths for which those variables remain observable. A bottom-up analysis of this graph allows one to compute reliability functions which evaluate the robustness of the observability property with respect to sensor failures. The design of optimal sensor networks thus resumes to finding pseudo-minimal sensor sets such that the mean time before losing the observability property is larger than a pre-defined value.

Abstract: We use graphical models to explore the question of how people learn simple causal relationships from data. The two leading psychological theories can both be seen as estimating the parameters of a fixed graph. We argue that a complete account of causal induction should also consider how people learn the underlying causal graph structure, and we propose to model this inductive process as a Bayesian inference. Our argument is supported through the discussion of three data sets.

Abstract: The paper compares two popular strategies for solving propositional satisfiability, i>backtracking search and i>resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the “width” (i>wa) of the problem"s graph. Our empirical evaluation confirms theoretical prediction, showing that on low-i>wa problems DR is very efficient, greatly outperforming the backtracking-based Davis–Putnam–Logemann–Loveland procedure (DP). We also emphasize the knowledge-compilation properties of DR and extend it to a tree-clustering algorithm that facilitates query answering. Finally, we propose two hybrid algorithms that combine the advantages of both DR and DP. These algorithms use control parameters that bound the complexity of resolution and allow time/space trade-offs that can be adjusted to the problem structure and to the user"s computational resources. Empirical studies demonstrate the advantages of such hybrid schemes.

Abstract: We present a discussion and initial empirical investigation of user-interface designs for a set of three Web browsers. The target end-user population we identified were experienced software engineers who maintained large Web sites or portals. The user study demonstrated the strengths and weaknesses of two conventional 2D browsers for this target user, as well as that of XML3D, a novel browser that integrates an interactive 3D hyperbolic graph view with a more traditional 2D list view of the data. A standard collapse/expand tree browser and a Web-based hierarchical categorization similar to Yahoo!, were competitively evaluated against XML3D. No reliable difference between the two 2D browsers was observed. However, the results showed clear differences between XML3D and the 2D user interfaces combined. With XML3D, participants performed search tasks within existing categories reliably faster with no decline in the quality of their responses. It was informally observed that integrating the ability to view the overall structure of the information space with the ability to easily assess local and global relationships was key to successful search performance. XML3D was the only tool of the three that efficiently showed the overall structure within one visualization. The XML3D browser accomplished this by combining a 3D graph layout view as well as an accompanying 2D list view. Users did opt to use the 2D user-interface components of XML3D during new category search tasks, and the XML3D performance advantage was no longer obtained in those conditions. In addition, there were no reliable differences in overall user satisfaction across the three user-interface designs. Since we observed subjects using the XML3D features differently depending on the kind of search task, future studies should explore optimal ways of integrating the use of novel focus+context visualizations and 2D lists for effective information retrieval. The contribution of this paper is that it includes empirical data to demonstrate where novel focus+context views might benefit experienced users over and above more conventional user-interface techniques, in addition to where design improvements are warranted.

Abstract: I present an introduction to some of the concepts within Bayesian networks to help a beginner become familiar with this field's theory. Bayesian networks are a combination of two different mathematical areas: graph theory and probability theory. So, I first give the basic definition of Bayesian networks. This is followed by an elaboration of the underlying graph theory that involves the arrangements of nodes and edges in a graph. Since Bayesian networks encode one's beliefs for a system of variables, I then proceed to discuss, in general, how to update these beliefs when one or more of the variables' values are no longer unknown (i.e., you have observed their values). Learning algorithms involve a combination of learning the probability distributions along with learning the network topology. I then conclude Part I by showing how Bayesian networks can be used in various domains, such as in the time-series problem of automatic speech recognition. In Part II I then give in more detail some of the algorithms needed for working with Bayesian networks.