3,494 research outputs found

    Structural graph matching using the EM algorithm and singular value decomposition

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    This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method

    Anonymizing Social Graphs via Uncertainty Semantics

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    Rather than anonymizing social graphs by generalizing them to super nodes/edges or adding/removing nodes and edges to satisfy given privacy parameters, recent methods exploit the semantics of uncertain graphs to achieve privacy protection of participating entities and their relationship. These techniques anonymize a deterministic graph by converting it into an uncertain form. In this paper, we propose a generalized obfuscation model based on uncertain adjacency matrices that keep expected node degrees equal to those in the unanonymized graph. We analyze two recently proposed schemes and show their fitting into the model. We also point out disadvantages in each method and present several elegant techniques to fill the gap between them. Finally, to support fair comparisons, we develop a new tradeoff quantifying framework by leveraging the concept of incorrectness in location privacy research. Experiments on large social graphs demonstrate the effectiveness of our schemes

    Distributed PCP Theorems for Hardness of Approximation in P

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    We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying assignment x{0,1}nx \in \{0,1\}^n to a CNF formula φ\varphi is shared between two parties, where Alice knows x1,,xn/2x_1, \dots, x_{n/2}, Bob knows xn/2+1,,xnx_{n/2+1},\dots,x_n, and both parties know φ\varphi. The goal is to have Alice and Bob jointly write a PCP that xx satisfies φ\varphi, while exchanging little or no information. Unfortunately, this model as-is does not allow for nontrivial query complexity. Instead, we focus on a non-deterministic variant, where the players are helped by Merlin, a third party who knows all of xx. Using our framework, we obtain, for the first time, PCP-like reductions from the Strong Exponential Time Hypothesis (SETH) to approximation problems in P. In particular, under SETH we show that there are no truly-subquadratic approximation algorithms for Bichromatic Maximum Inner Product over {0,1}-vectors, Bichromatic LCS Closest Pair over permutations, Approximate Regular Expression Matching, and Diameter in Product Metric. All our inapproximability factors are nearly-tight. In particular, for the first two problems we obtain nearly-polynomial factors of 2(logn)1o(1)2^{(\log n)^{1-o(1)}}; only (1+o(1))(1+o(1))-factor lower bounds (under SETH) were known before

    Un algorithme Hongrois pour l'appariement de graphes avec correction d'erreurs

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    International audienceBipartite graph matching algorithms become more and more popular to solve error-correcting graph matching problems and to approximate the graph edit distance of two graphs. However, the memory requirements and execution times of this method are respectively proportional to (n + m) 2 and (n + m) 3 where n and m are the order of the graphs. Subsequent developments reduced these complexities. However , these improvements are valid only under some constraints on the parameters of the graph edit distance. We propose in this paper a new formulation of the bipartite graph matching algorithm designed to solve efficiently the associated graph edit distance problem. The resulting algorithm requires O(nm) memory space and O(min(n, m) 2 max(n, m)) execution times.L'appariement de graphes biparti deviennent de plus en plus populaires pour résoudre des problèmes d'appariement de graphes avec correction d'erreurs et pour approximer la distance d'édition sur graphes. Cependant, les exigences en mémoire et temps de calcul de cette méthode sont respectivement proportionnels à (n + m)^2 et (n + m)^3 où n et m représentent la taille des deux graphes. Des développements ultérieurs ont réduit ces complexités. Cependant, ces améliorations ne sont valables que sous certaines contraintes sur les paramètres de la distance d'édition. Nous proposons dans cet article une nouvelle formulation de l'algorithme Hongrois conçu pour résoudre efficacement le problème de distance d'édition associé. L'algorithme résultat nécessite un espace mémoire O (nm) et des temps d'exécution O (min (n, m)^2 max (n, m))
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