Conditional Reliability in Uncertain Graphs

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of existence. Many approaches and problem variants have been considered in the literature, all assuming that edge-existence probabilities are fixed. Nevertheless, in real-world graphs, edge probabilities typically depend on external conditions. In metabolic networks a protein can be converted into another protein with some probability depending on the presence of certain enzymes. In social influence networks the probability that a tweet of some user will be re-tweeted by her followers depends on whether the tweet contains specific hashtags. In transportation networks the probability that a network segment will work properly or not might depend on external conditions such as weather or time of the day. In this paper we overcome this limitation and focus on conditional reliability, that is assessing reliability when edge-existence probabilities depend on a set of conditions. In particular, we study the problem of determining the k conditions that maximize the reliability between two nodes. We deeply characterize our problem and show that, even employing polynomial-time reliability-estimation methods, it is NP-hard, does not admit any PTAS, and the underlying objective function is non-submodular. We then devise a practical method that targets both accuracy and efficiency. We also study natural generalizations of the problem with multiple source and target nodes. An extensive empirical evaluation on several large, real-life graphs demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure

ProbTree: a query-efficient representation of probabilistic graphs

Technical PaperInformation in many applications, such as mobile wireless systems, social networks, and road networks, is captured by graphs, in many cases uncertain. We study the problem of querying a probabilistic graph; in particular, we examine source-to-target' queries, such as computing the shortest path between two vertices. Evaluating ST-queries over probabilistic graphs is #P-hard, as it requires examining an exponential number of possible worlds'. Existing solutions to the ST-query problem, which sample possible worlds, have two downsides: (i) many samples are needed for reasonable accuracy, and (ii) a possible world can be very large. To tackle these issues, we study the ProbTree, a data structure that stores a succinct representation of the probabilistic graph. Existing ST-query solutions are executed on top of this structure, with the number of samples and possible world sizes reduced.postprin

An Indexing Framework for Queries on Probabilistic Graphs

postprin

Node Classification in Uncertain Graphs

In many real applications that use and analyze networked data, the links in the network graph may be erroneous, or derived from probabilistic techniques. In such cases, the node classification problem can be challenging, since the unreliability of the links may affect the final results of the classification process. If the information about link reliability is not used explicitly, the classification accuracy in the underlying network may be affected adversely. In this paper, we focus on situations that require the analysis of the uncertainty that is present in the graph structure. We study the novel problem of node classification in uncertain graphs, by treating uncertainty as a first-class citizen. We propose two techniques based on a Bayes model and automatic parameter selection, and show that the incorporation of uncertainty in the classification process as a first-class citizen is beneficial. We experimentally evaluate the proposed approach using different real data sets, and study the behavior of the algorithms under different conditions. The results demonstrate the effectiveness and efficiency of our approach

Injecting Uncertainty in Graphs for Identity Obfuscation

Data collected nowadays by social-networking applications create fascinating opportunities for building novel services, as well as expanding our understanding about social structures and their dynamics. Unfortunately, publishing social-network graphs is considered an ill-advised practice due to privacy concerns. To alleviate this problem, several anonymization methods have been proposed, aiming at reducing the risk of a privacy breach on the published data, while still allowing to analyze them and draw relevant conclusions. In this paper we introduce a new anonymization approach that is based on injecting uncertainty in social graphs and publishing the resulting uncertain graphs. While existing approaches obfuscate graph data by adding or removing edges entirely, we propose using a finer-grained perturbation that adds or removes edges partially: this way we can achieve the same desired level of obfuscation with smaller changes in the data, thus maintaining higher utility. Our experiments on real-world networks confirm that at the same level of identity obfuscation our method provides higher usefulness than existing randomized methods that publish standard graphs.Comment: VLDB201