Showing papers on "Graph (abstract data type) published in 2002"

Markov chain Monte Carlo estimation of exponential random graph models

Abstract: This paper is about estimating the parameters of the exponential random graph model, also known as the p∗ model, using frequentist Markov chain Monte Carlo (MCMC) methods The exponential random graph model is simulated using Gibbs or MetropolisHastings sampling The estimation procedures considered are based on the Robbins-Monro algorithm for approximating a solution to the likelihood equation A major problem with exponential random graph models resides in the fact that such models can have, for certain parameter values, bimodal (or multimodal) distributions for the sufficient statistics such as the number of ties The bimodality of the exponential graph distribution for certain parameter values seems a severe limitation to its practical usefulness The possibility of bior multimodality is reflected in the possibility that the outcome space is divided into two (or more) regions such that the more usual type of MCMC algorithms, updating only single relations, dyads, or triplets, have extremely long sojourn times within such regions, and a negligible probability to move from one region to another In such situations, convergence to the target distribution is extremely slow To be useful, MCMC algorithms must be able to make transitions from a given graph to a very different graph It is proposed to include transitions to the graph complement as updating steps to improve the speed of convergence to the target distribution Estimation procedures implementing these ideas work satisfactorily for some data sets and model specifications, but not for all

A survey of graph layout problems

Abstract: Graph layout problems are a particular class of combinatorial optimization problems whose goal is to find a linear layout of an input graph in such way that a certain objective cost is optimized. This survey considers their motivation, complexity, approximation properties, upper and lower bounds, heuristics and probabilistic analysis on random graphs. The result is a complete view of the current state of the art with respect to layout problems from an algorithmic point of view.

The strong perfect graph theorem

Abstract: A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The "strong perfect graph conjecture" (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by Conforti, Cornuejols and Vuskovic -- that every Berge graph either falls into one of a few basic classes, or it has a kind of separation that cannot occur in a minimal imperfect graph. In this paper we prove both these conjectures.

Modeling and Solving the Train Timetabling Problem

Abstract: The train timetabling problem aims at determining a periodic timetable for a set of trains that does not violate track capacities and satisfies some operational constraints. In particular, we concentrate on the problem of a single, one-way track linking two major stations, with a number of intermediate stations in between. Each train connects two given stations along the track (possibly different from the two major stations) and may have to stop for a minimum time in some of the intermediate stations. Trains can overtake each other only in correspondence of an intermediate station, and a minimum time interval between two consecutive departures and arrivals of trains in each station is specified.In this paper, we propose a graph theoretic formulation for the problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant. This formulation is used to derive an integer linear programming model that is relaxed in a Lagrangian way. A novel feature of our model is that the variables in the relaxed constraints are associated only with nodes (as opposed to arcs) of the aforementioned graph. This allows a considerable speed-up in the solution of the relaxation. The relaxation is embedded within a heuristic algorithm which makes extensive use of the dual information associated with the Lagrangian multipliers. We report extensive computational results on real-world instances provided from Ferrovie dello Stato SpA, the Italian railway company, and from Ansaldo Segnalamento Ferroviario SpA.

Two formal analyses of attack graphs

Abstract: An attack graph is a succinct representation of all paths through a system that end in a state where an intruder has successfully achieved his goal. Today Red Teams determine the vulnerability of networked systems by drawing gigantic attack graphs by hand. Constructing attack graphs by hand is tedious, error-prone, and impractical for large systems. By viewing an attack as a violation of a safety property, we can use off-the-shelf model checking technology to produce attack graphs automatically: a successful path from the intruder's viewpoint is a counterexample produced by the model checker In this paper we present an algorithm for generating attack graphs using model checking as a subroutine. Security analysts use attack graphs for detection, defense and forensics. In this paper we present a minimization analysis technique that allows analysts to decide which minimal set of security measures would guarantee the safety of the system. We provide a formal characterization of this problem: we prove that it is polynomially equivalent to the minimum hitting set problem and we present a greedy algorithm with provable bounds. We also present a reliability analysis technique that allows analysts to perform a simple cost-benefit trade-off depending on the likelihoods of attacks. By interpreting attack graphs as Markov Decision Processes we can use the value iteration algorithm to compute the probabilities of intruder success for each attack the graph.

Methods and apparatus for decoding ldpc codes

Abstract: Methods and apparatus for decoding codewords using message passing decoding techniques which are particularly well suited for use with low density parity check (LDPC) codes and long codewords are described. The described methods allow decoding graph structures which are largely comprised of multiple identical copies of a much smaller graph. Copies of the smaller graph are subject to a controlled permutation operation to create the larger graph structure. The same controlled permutations are directly implemented to support message passing between the replicated copies of the small graph. Messages corresponding to individual copies of the graph are stored in a memory and accessed in sets, one from each copy of the graph, using a SIMD read or write instruction. The graph permutation operation may be implemented by simply reordering messages, e.g., using a cyclic permutation operation, in each set of messages read out of a message memory so that the messages are passed to processing circuits corresponding to different copies of the small graph.

Graph models for waves in thin structures

Abstract: A brief survey on graph models for wave propagation in thin structures is presented. Such models arise in many areas of mathematics, physics, chemistry and engineering (dynamical systems, nanotechnology, mesoscopic systems, photonic crystals etc). Considerations are limited to spectral problems, although references to works with other studies are provided.

Metrics for Graph Drawing Aesthetics

Abstract: Graph layout algorithms typically conform to one or more aesthetic criteria (e.g. minimizing the number of bends, maximizing orthogonality). Determining the extent to which a graph drawing conforms to an aesthetic criterion tends to be done informally, and varies between different algorithms. This paper presents formal metrics for measuring the aesthetic presence in a graph drawing for seven common aesthetic criteria, applicable to any graph drawing of any size. The metrics are useful for determining the aesthetic quality of a given graph drawing, or for defining a cost function for genetic algorithms or simulated annealing programs. The metrics are continuous, so that aesthetic quality is not stated as a binary conformance decision (i.e. the drawing either conforms to the aesthetic or not), but can be stated as the extent of aesthetic conformance using a number between 0 and 1. The paper presents the seven metric formulae. The application of these metrics is demonstrated through the aesthetic analysis of example graph drawings produced by common layout algorithms.

Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks

Abstract: We present a series of approximation algorithms for finding a small weakly-connected dominating set (WCDS) in a given graph to be used in clustering mobile ad hoc networks. The structure of a graph can be simplified using WCDS's and made more succinct for routing in ad hoc networks. The theoretical performance ratio of these algorithms is O(ln Δ) compared to the minimum size WCDS, where Δ is the maximum degree of the input graph. The first two algorithms are based on the centralized approximation algorithms of Guha and Khuller cite guha-khuller-1998 for finding small connected dominating sets (CDS's). The main contribution of this work is a completely distributed algorithm for finding small WCDS's and the performance of this algorithm is shown to be very close to that of the centralized approach. Comparisons between our work and some previous work (CDS-based) are also given in terms of the size of resultant dominating sets and graph connectivity degradation.

All pairs shortest paths using bridging sets and rectangular matrix multiplication

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.

Global organization of the Wordnet lexicon

Abstract: The lexicon consists of a set of word meanings and their semantic relationships. A systematic representation of the English lexicon based in psycholinguistic considerations has been put together in the database Wordnet in a long-term collaborative effort. We present here a quantitative study of the graph structure of Wordnet to understand the global organization of the lexicon. Semantic links follow power-law, scale-invariant behaviors typical of self-organizing networks. Polysemy (the ambiguity of an individual word) is one of the links in the semantic network, relating the different meanings of a common word. Polysemous links have a profound impact in the organization of the semantic graph, conforming it as a small world network, with clusters of high traffic (hubs) representing abstract concepts such as line, head, or circle. Our results show that: (i) Wordnet has global properties common to many self-organized systems, and (ii) polysemy organizes the semantic graph in a compact and categorical representation, in a way that may explain the ubiquity of polysemy across languages.

Methods and systems for automated semantic knowledge leveraging graph theoretic analysis and the inherent structure of communication

Abstract: A system that processes a collection of one or more documents and thereby constructs a knowledge base is described. The system leverages innovative graph theoretical analysis of documents leveraging the inherent structure in communication. Through the generation of the automated knowledge base the system is able to provides intra-document analysis such as variable summarization and indexing, document key concepts, better filtering and relevance matching on a semantic level for documents, context dependant directories, document categorization, better basis for natural language processing, new knowledge and information through the amalgamation of the data (collection intelligence).

A graph model for unsupervised lexical acquisition

Abstract: This paper presents an unsupervised method for assembling semantic knowledge from a part-of-speech tagged corpus using graph algorithms. The graph model is built by linking pairs of words which participate in particular syntactic relationships. We focus on the symmetric relationship between pairs of nouns which occur together in lists. An incremental cluster-building algorithm using this part of the graph achieves 82% accuracy at a lexical acquisition task, evaluated against WordNet classes. The model naturally realises domain and corpus specific ambiguities as distinct components in the graph surrounding an ambiguous word.

GraphGrep: A fast and universal method for querying graphs

Abstract: GraphGrep is an application-independent method for querying graphs, finding all the occurrences of a subgraph in a database of graphs. The interface to GraphGrep is a regular expression graph query language Glide that combines features from Xpath and Smart. Glide incorporates both single node and variable-length wildcards. Our algorithm uses hash-based fingerprinting to represent the graphs in an abstract form and to filter the database. GraphGrep has been tested on databases of size up to 16,000 molecules and performs well in this entire range.

A graph-based recommender system for digital library

Abstract: Research shows that recommendations comprise a valuable service for users of a digital library [11] While most existing recommender systems rely either on a content-based approach or a collaborative approach to make recommendations, there is potential to improve recommendation quality by using a combination of both approaches (a hybrid approach) In this paper, we report how we tested the idea of using a graph-based recommender system that naturally combines the content-based and collaborative approaches Due to the similarity between our problem and a concept retrieval task, a Hopfield net algorithm was used to exploit high-degree book-book, user-user and book-user associations Sample hold-out testing and preliminary subject testing were conducted to evaluate the system, by which it was found that the system gained improvement with respect to both precision and recall by combining content-based and collaborative approaches However, no significant improvement was observed by exploiting high-degree associations

Splicing graphs and EST assembly problem.

Abstract: Motivation: The traditional approach to annotate alternative splicing is to investigate every splicing variant of the gene in a case-by-case fashion. This approach, while useful, has some serious shortcomings. Recent studies indicate that alternative splicing is more frequent than previously thought and some genes may produce tens of thousands of different transcripts. A list of alternatively spliced variants for such genes would be difficult to build and hard to analyse. Moreover, such a list does not show the relationships between different transcripts and does not show the overall structure of all transcripts. A better approach would be to represent all splicing variants for a given gene in a way that captures the relationships between different splicing variants. Results: We introduce the notion of the splicing graph that is a natural and convenient representation of all splicing variants. The key difference with the existing approaches is that we abandon the linear (sequence) representation of each transcript and replace it with a graph representation where each transcript corresponds to a path in the graph. We further design an algorithm to assemble EST reads into the splicing graph rather than assembling them into each splicing variant in a case-by-case fashion. Availability:

Advanced Topics in Database Research

Abstract: Database applications features such as Structured Query Language programming, exception handling, integrity constraints, and table triggers pose difficulties for maintenance activities, especially for regression testing that follows modifying database applications. In this chapter, we address these difficulties and propose a two-phase regression testing methodology. In phase 1, we explore control flow and data flow analysis issues of database applications. Then, we propose an impact analysis technique that is based on dependencies that exist among the components of database applications. This analysis leads to selecting test cases from the initial test suite for regression testing the modified application. In phase 2, we propose two algorithms for reducing the number of regression test cases. The Graph Walk algorithm walks through the control flow graph of database modules and selects a safe set of test cases to retest. The Call Graph Firewall algorithm uses a firewall for the inter-procedural level. Our experience with this regression testing methodology shows that the impact analysis technique is adequate for selecting regression tests and that phase 2 techniques can be used for further reduction in the number of these tests.

System and method for monitoring performance metrics

Abstract: A system and method for monitoring a set of performance metrics is described. The methods include metric correlation and grouping methods that analyze a group of temporally related metrics, and correlate pairs of the metrics in the group. In one embodiment, rank correlation techniques are used to perform this correlation. Methods are also described for grouping metrics using a dynamic correlation pair graph that preserves all of the correlated relationships. This correlation pair graph may be used to determine which metrics are associated with a particular key metric, which may provide information on the cause of an alarm or other event involving the key metric. Another embodiment includes apparatus for correlating, grouping, and identifying the metrics.

An efficient distributed algorithm for constructing small dominating sets

Abstract: The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem.We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in O(log n log Δ) rounds with high probability, where n is the number of nodes, Δ is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within O (log Δ) of the optimal in expectation and within O(log n) of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements.

Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses

Abstract: Traditional hardness versus randomness results focus on time-efficient randomized decision procedures. We generalize these trade-offs to a much wider class of randomized processes. We work out various applications, most notably to derandomizing Arthur-Merlin games. We show that every language with a bounded round Arthur-Merlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomial-time hierarchy (and hence the polynomial-time hierarchy collapses). Since the graph nonisomorphism problem has a bounded round Arthur-Merlin game, this provides the first strong evidence that graph nonisomorphism has subexponential size proofs. We also establish hardness versus randomness trade-offs for space bounded computation.

Method and system for preloading resources

Abstract: A method and system for preloading data is provided. Resources are preloaded on a client before they are needed by an application. Application hints and static resources lists may be used to indicate resources are needed. The application may begin execution before receiving all of the resources associated with the application. Preloading may be done during execution of an application, or when the application is not executing. Preloading allows an application to run smoothly without consuming more resources than are needed by an application. A prediction graph may be generated that is used in predicting the resources that are likely to be needed by the application. An analyzer may also be used to simulate the system and adjust parameters used in creating the prediction graph.

Algorithmic aspects of topology control problems for ad hoc networks

Abstract: Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called textbf monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be bf NP -complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is obtained. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.

Empirical Evaluation of Aesthetics-based Graph Layout

Abstract: Many automatic graph layout algorithms have been designed and implemented to display relational data in a graphical (usually node-arc) manner. The success of these algorithms is typically measured by their computational efficiency and the extent to which they conform to aesthetic criteria (for example, minimising the number of crossings, maximising symmetry). Little research has been performed on the usability aspects of such algorithms: do they produce graph drawings that make the embodied information easy to use and understandq Is the computational effort expended on conforming to the assumed aesthetic criteria justifiable with respect to better usabilityq This paper reports on usability studies that were performed to investigate the merit of automatic graph layout algorithms with respect to human use. The paper describes three ways in which this issue has been considered experimentally: first, investigating individual aesthetic criteria in simple, abstract graph structures; second, investigating the results of common automatic graph layout algorithms; and third, investigating individual aesthetic criteria and other relevant secondary notations in Unified Modeling Language class and collaboration diagrams. The results show that the use of only some aesthetics affect usability significantly, and that the semantic domain of the graph drawings affects which aesthetic criteria need to be emphasised.

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.

Towards pattern-based design recovery

Abstract: A method and a corresponding tool is described which assist design recovery and program understanding by recognising instances of design patterns semi-automatically. The approach taken is specifically designed to overcome the existing scalability problems caused by many design and implementation variants of design pattern instances. Our approach is based on a new recognition algorithm which works incrementally rather than trying to analyse a possibly large software system in one pass without any human intervention. The new algorithm exploits domain and context knowledge given by a reverse engineer and by a special underlying data structure, namely a special form of an annotated abstract syntax graph. A comparative and quantitative evaluation of applying the approach to the Java AWT and JGL libraries is also given.

Optical character recognition for cursive handwriting

Abstract: A new analytic scheme, which uses a sequence of image segmentation and recognition algorithms, is proposed for the off-line cursive handwriting recognition problem. First, some global parameters, such as slant angle, baselines, stroke width and height, are estimated. Second, a segmentation method finds character segmentation paths by combining gray-scale and binary information. Third, a hidden Markov model (HMM) is employed for shape recognition to label and rank the character candidates. For this purpose, a string of codes is extracted from each segment to represent the character candidates. The estimation of feature space parameters is embedded in the HMM training stage together with the estimation of the HMM model parameters. Finally, information from a lexicon and from the HMM ranks is combined in a graph optimization problem for word-level recognition. This method corrects most of the errors produced by the segmentation and HMM ranking stages by maximizing an information measure in an efficient graph search algorithm. The experiments indicate higher recognition rates compared to the available methods reported in the literature.

Tutorial Introduction to Graph Transformation: A Software Engineering Perspective

Abstract: We give an introduction to graph transformation, not only for researchers in software engineering, but based on applications of graph transformation in this domain. In particular, we demonstrate the use of graph transformation to model object- and component-based systems and to specify syntax and semantics of diagram languages. Along the way we introduce the basic concepts, discuss different approaches, and mention relevant theory and tools.

Self-similarity in the web

Abstract: Algorithmic tools for searching and mining the Web are becoming increasingly sophisticated and vital. In this context, algorithms that use and exploit structural information about the Web perform better than generic methods in both efficiency and reliability.We present an extensive characterization of the graph structure of the Web, with a view to enabling high-performance applications that make use of this structure. In particular, we show that the Web emerges as the outcome of a number of essentially independent stochastic processes that evolve at various scales. A striking consequence of this scale invariance is that the structure of the Web is "fractal"---cohesive subregions display the same characteristics as the Web at large. An understanding of this underlying fractal nature is therefore applicable to designing data services across multiple domains and scales.We describe potential applications of this line of research to optimized algorithm design for Web-scale data analysis.