395 research outputs found

    Compact Labelings For Efficient First-Order Model-Checking

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    We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \emph{nicely locally cwd-decomposable}. This notion generalizes that of a \emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \emph{clique-width} with limited overlaps. We also consider such labelings for \emph{bounded} first-order formulas on graph classes of \emph{bounded expansion}. Some of these results are extended to counting queries

    Path Queries on Compressed XML

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    Central to any XML query language is a path language such as XPath which operates on the tree structure of the XML document. We demonstrate in this paper that the tree structure can be e#ectively compressed and manipulated using techniques derived from symbolic model checking . Specifically, we show first that succinct representations of document tree structures based on sharing subtrees are highly e#ective. Second, we show that compressed structures can be queried directly and e#ciently through a process of manipulating selections of nodes and partial decompression

    Pruning based Distance Sketches with Provable Guarantees on Random Graphs

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    Measuring the distances between vertices on graphs is one of the most fundamental components in network analysis. Since finding shortest paths requires traversing the graph, it is challenging to obtain distance information on large graphs very quickly. In this work, we present a preprocessing algorithm that is able to create landmark based distance sketches efficiently, with strong theoretical guarantees. When evaluated on a diverse set of social and information networks, our algorithm significantly improves over existing approaches by reducing the number of landmarks stored, preprocessing time, or stretch of the estimated distances. On Erd\"{o}s-R\'{e}nyi graphs and random power law graphs with degree distribution exponent 2<β<32 < \beta < 3, our algorithm outputs an exact distance data structure with space between Θ(n5/4)\Theta(n^{5/4}) and Θ(n3/2)\Theta(n^{3/2}) depending on the value of β\beta, where nn is the number of vertices. We complement the algorithm with tight lower bounds for Erdos-Renyi graphs and the case when β\beta is close to two.Comment: Full version for the conference paper to appear in The Web Conference'1

    Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models

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    We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.Comment: 26 pages, 17 figure

    Even Delta-Matroids and the Complexity of Planar Boolean CSPs

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    The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Δ\Delta-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Using a reduction to even Δ\Delta-matroids, we then extend the tractability result to larger classes of Δ\Delta-matroids that we call efficiently coverable. It properly includes classes that were known to be tractable before, namely co-independent, compact, local, linear and binary, with the following caveat: we represent Δ\Delta-matroids by lists of tuples, while the last two use a representation by matrices. Since an n×nn\times n matrix can represent exponentially many tuples, our tractability result is not strictly stronger than the known algorithm for linear and binary Δ\Delta-matroids.Comment: 33 pages, 9 figure

    Defect tolerance: fundamental limits and examples

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    This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems, in which the defective objects are replaced by the judiciously connected redundant objects. The fundamental limits of this model are characterized under various asymptotic settings and both asymptotic and finite-size systems that approach these limits are constructed. Among other results, we show that the simple modular redundancy is in general suboptimal. As we develop, this combinatorial problem of defect tolerant system design has a natural interpretation as one of graph coloring, and the analysis is significantly different from that traditionally used in information redundancy for error-control codes.©201

    Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure

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    Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of varying numbers of tori and Klein bottles in the 4-sphere. Finite covers of some of those manifolds are then shown to be complements of tori and Klein bottles in other simply-connected closed 4-manifolds. All the examples are based on a construction of Ratcliffe and Tschantz, who produced 1171 noncompact hyperbolic 4-manifolds of minimal volume. Our examples are finite covers of some of those manifolds.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-41.abs.htm
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