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.

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.

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.

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.

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.

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.

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.

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: 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.

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.

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).

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.

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.

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:

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.

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.

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.

Abstract: This paper addresses the problem of large scale multiview registration of range images captured from unknown viewing directions. To reduce the computational burden, we decouple the local problem of pairwise registration on neighboring views from the global problem of distribution of accumulated errors. We define the global problem over the graph of neighboring views, and we show that this graph can be decomposed into a set of cycles such that the optimal transformation parameters for each cycle can be solved in closed form. We then describe an iterative procedure that can be used to integrate the solutions for the set of cycles across the graph. This method for error distribution does not require point correspondences between views, and therefore can be used together with robot odometry or any method of pairwise registration. Experimental results demonstrate the effectiveness of this technique on range images of an indoor facility.

Abstract: The Web graph is a giant social network whose properties have been measured and modeled extensively in recent years. Most such studies concentrate on the graph structure alone, and do not consider textual properties of the nodes. Consequently, Web communities have been characterized purely in terms of graph structure and not on page content. We propose that a topic taxonomy such as Yahoo! or the Open Directory provides a useful framework for understanding the structure of content-based clusters and communities. In particular, using a topic taxonomy and an automatic classifier, we can measure the background distribution of broad topics on the Web, and analyze the capability of recent random walk algorithms to draw samples which follow such distributions. In addition, we can measure the probability that a page about one broad topic will link to another broad topic. Extending this experiment, we can measure how quickly topic context is lost while walking randomly on the Web graph. Estimates of this topic mixing distance may explain why a global PageRank is still meaningful in the context of broad queries. In general, our measurements may prove valuable in the design of community-specific crawlers and link-based ranking systems.

Abstract: Currently, an important issue in power distribution is the need to optimize medium voltage (MV) networks serving urban areas. This paper shows how an evolutionary algorithm can be used as the basis for the type of efficient algorithm such optimization demands. The search for optimal network solution will be restricted to a graph defined from the urban map, so each graph branch represents a trench. The solution space (networks) is assumed with "loop feeder circuits": networks with two electrical paths from the high voltage/medium voltage (HV/MV) substations to the customers. In the optimization process, the investment and loss load costs are considered taking into account the constraints of conductor capacities and voltage drop. The investment costs will take into account that some cables can be lying in the same trench. The process was applied for a Spanish city of 200,000 inhabitants.

Abstract: A relationship graph of nodes representing entities and edges representing relationships among the entities is searched to find a match on search criteria, such as an individual or a company. Paths through the relationship graph to the match are identified and a relevance value is associated with each path. A node in each path is specified as a connector for the path. The connectors and relevance values may be displayed to allow a choice of paths. If more than one match is found, a selection may be made by a user. Additionally, any matches may be filtered according to privacy rules.

Abstract: Methods and data processing system readable media have been created to graph user clickstream data over a network or at a network site to yield meaningful and visually esthetic information. In one set of embodiments, the method can comprise (i) performing a significance test on data from a network log and generating significance results. The method can also comprise (ii) determining which of network addresses and clicktrails between network addresses meet a traffic flow criterion. The data that meet a significance criterion, traffic criterion, or both can form (iii) graphable addresses and relationships. The method can further comprise (iv) generating statistics about the graphable addresses and relationships. The method can still further comprise (v) generating a graph based on the statistics about the graphable addresses and relationships, and (vi) changing any or all of the traffic flow, significance criterion, and statistics being computed, and regenerating the graph.

Abstract: Trajectory design for high-dimensional systems with nonconvex constraints has considerable success recently; however, the resolution completeness analysis for various methods is insufficient. In this paper, based on Lipschitz condition and the accessibility graph, conditions for resolution completeness are derived. By combining the systematic search with randomized technique, a randomized planner is transformed to be a deterministic resolution complete planner, which shows reliable performance in the simulation.

Abstract: We provide a theoretical framework that consists of graph theoretical and Lyapunov-based approaches to stability analysis and distributed control of multi-agent formations. This framework relays on the notion of graph rigidity as a means of identifying the shape variables of a formation. Using this approach, we can formally define formations of multiple vehicles and three types of stabilization/tracking problems for dynamic multi-agent systems. We show how these three problems can be addressed mutually independent of each other for a formation of two agents. Then, we introduce a procedure called dynamic node augmentation that allows construction of a larger formation with more agents that can be rendered structurally stable in a distributed manner from some initial formation that is structurally stable. We provide two examples of formations that can be controlled using this approach, namely, the V-formation and the diamond formation.

Abstract: The Web graph is a giant social network whose properties have been measured and modeled extensively in recent years. Most such studies concentrate on the graph structure alone, and do not consider textual properties of the nodes. Consequently, Web communities have been characterized purely in terms of graph structure and not on page content. We propose that a topic taxonomy such as Yahoo! or the Open Directory provides a useful framework for understanding the structure of content-based clusters and communities. In particular, using a topic taxonomy and an automatic classifier, we can measure the background distribution of broad topics on the Web, and analyze the capability of recent random walk algorithms to draw samples which follow such distributions. In addition, we can measure the probability that a page about one broad topic will link to another broad topic. Extending this experiment, we can measure how quickly topic context is lost while walking randomly on the Web graph. Estimates of this topic mixing distance may explain why a global PageRank is still meaningful in the context of broad queries. In general, our measurements may prove valuable in the design of community-specific crawlers and link-based ranking systems.