Misael Mongiovì

Mining Heavy Subgraphs in Time-Evolving Networks

Networks from different genres are not static entities, but exhibit dynamic behavior. The congestion level of links in transportation networks varies in time depending on the traffic. Similarly, social and communication links are employed at varying rates as information cascades unfold. In recent years there has been an increase of interest in modeling and mining dynamic networks. However, limited attention has been placed in high-scoring sub graph discovery in time-evolving networks. We define the problem of finding the highest-scoring temporal sub graph in a dynamic network, termed Heaviest Dynamic Sub graph (HDS). We show that HDS is NP-hard even with edge weights in {-1,1} and devise an efficient approach for large graph instances that evolve over long time periods. While a naive approach would enumerate all O(t^2) sub-intervals, our solution performs an effective pruning of the sub-interval space by considering O(t*log(t)) groups of sub-intervals and computing an aggregate of each group in logarithmic time. We also define a fast heuristic and a tight upper bound for approximating the static version of HDS, and use them for further pruning the sub-interval space and quickly verifying candidate sub-intervals. We perform an extensive experimental evaluation of our algorithm on transportation, communication and social media networks for discovering sub graphs that correspond to traffic congestions, communication overflow and localized social discussions. Our method is two orders of magnitude faster than a naive approach and scales well with network size and time length.

SIGMA: A SET-COVER-BASED INEXACT GRAPH MATCHING ALGORITHM ∗

Network querying is a growing domain with vast applications ranging from screening compounds against a database of known molecules to matching sub-networks across species. Graph indexing is a powerful method for searching a large database of graphs. Most graph indexing methods to date tackle the exact matching (isomorphism) problem, limiting their applicability to specific instances in which such matches exist. Here we provide a novel graph indexing method to cope with the more general, inexact matching problem. Our method, SIGMA, builds on approximating a variant of the set-cover problem that concerns overlapping multi-sets. We extensively test our method and compare it to a baseline method and to the state-of-the-art Grafil. We show that SIGMA outperforms both, providing higher pruning power in all the tested scenarios.

Efficient multicasting for delay tolerant networks using graph indexing

In Delay Tolerant Networks (DTNs), end-to-end connectivity between nodes does not always occur due to limited radio coverage, node mobility and other factors. Remote communication may assist in guaranteeing delivery. However, it has a considerable cost, and consequently, minimizing it is an important task. For multicast routing, the problem is NP-hard, and naive approaches are infeasible on large problem instances. In this paper we define the problem of minimizing the remote communication cost for multicast in DTNs. Our formulation handles the realistic scenario in which a data source is continuously updated and nodes need to receive recent versions of data. We analyze the problem in the case of scheduled trajectories and known traffic demands, and propose a solution based on a novel graph indexing system. We also present an adaptive extension that can work with limited knowledge of node mobility. Our method reduces the search space significantly and finds an optimal solution in reasonable time. Extensive experimental analysis on large real and synthetic datasets shows that the proposed method completes in less than 10 seconds on datasets with millions of encounters, with an improvement of up to 100 times compared to a naive approach.

SING: Subgraph search In Non-homogeneous Graphs

BackgroundFinding the subgraphs of a graph database that are isomorphic to a given query graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism is a computationally hard problem, indexing techniques have been intensively exploited to speed up the process. Such systems filter out those graphs which cannot contain the query, and apply a subgraph isomorphism algorithm to each residual candidate graph. The applicability of such systems is limited to databases of small graphs, because their filtering power degrades on large graphs.ResultsIn this paper, SING (Subgraph search In Non-homogeneous Graphs), a novel indexing system able to cope with large graphs, is presented. The method uses the notion of feature, which can be a small subgraph, subtree or path. Each graph in the database is annotated with the set of all its features. The key point is to make use of feature locality information. This idea is used to both improve the filtering performance and speed up the subgraph isomorphism task.ConclusionsExtensive tests on chemical compounds, biological networks and synthetic graphs show that the proposed system outperforms the most popular systems in query time over databases of medium and large graphs. Other specific tests show that the proposed system is effective for single large graphs.

GraphFind: enhancing graph searching by low support data mining techniques.

BackgroundBiomedical and chemical databases are large and rapidly growing in size. Graphs naturally model such kinds of data. To fully exploit the wealth of information in these graph databases, a key role is played by systems that search for all exact or approximate occurrences of a query graph. To deal efficiently with graph searching, advanced methods for indexing, representation and matching of graphs have been proposed.ResultsThis paper presents GraphFind. The system implements efficient graph searching algorithms together with advanced filtering techniques that allow approximate search. It allows users to select candidate subgraphs rather than entire graphs. It implements an effective data storage based also on low-support data mining.ConclusionsGraphFind is compared with Frowns, GraphGrep and gIndex. Experiments show that GraphFind outperforms the compared systems on a very large collection of small graphs. The proposed low-support mining technique which applies to any searching system also allows a significant index space reduction.

Global alignment of protein-protein interaction networks.

Sequence-based comparisons have been the workhorse of bioinformatics for the past four decades, furthering our understanding of gene function and evolution. Over the last decade, a plethora of technologies have matured for measuring Protein-protein interactions (PPIs) at large scale, yielding comprehensive PPI networks for over ten species. In this chapter, we review methods for harnessing PPI networks to improve the detection of orthologous proteins across species. In particular, we focus on pairwise global network alignment methods that aim to find a mapping between the networks of two species that maximizes the sequence and interaction similarities between matched nodes. We further suggest a novel evolutionary-based global alignment algorithm. We then compare the different methods on a yeast-fly-worm benchmark, discuss their performance differences, and conclude with open directions for future research.

Fast analytical methods for finding significant labeled graph motifs

Network motif discovery is the problem of finding subgraphs of a network that occur more frequently than expected, according to some reasonable null hypothesis. Such subgraphs may indicate small scale interaction features in genomic interaction networks or intriguing relationships involving actors or a relationship among airlines. When nodes are labeled, they can carry information such as the genomic entity under study or the dominant genre of an actor. For that reason, labeled subgraphs convey information beyond structure and could therefore enjoy more applications. To identify statistically significant motifs in a given network, we propose an analytical method (i.e. simulation-free) that extends the works of Picard et al. (J Comput Biol 15(1):1–20, 2008) and Schbath et al. (J Bioinform Syst Biol 2009(1):616234, 2009) to label-dependent scale-free graph models. We provide an analytical expression of the mean and variance of the count under the Expected Degree Distribution random graph model. Our model deals with both induced and non-induced motifs. We have tested our methodology on a wide set of graphs ranging from protein–protein interaction networks to movie networks. The analytical model is a fast (usually faster by orders of magnitude) alternative to simulation. This advantage increases as graphs grow in size.

Making Android Apps Data-Leak-Safe by Data Flow Analysis and Code Injection

Some support is needed in order to shun the possibility that sensitive data handled by applications are sent to improper destinations. Although apps running on Android OS declare the accessed services, once the user accepts, the application receives complete permissions and may use sensitive data improperly. Some tools have emerged to check data access and flow, however such tools are either based on static analysis or dynamic tracking. The former brings no overhead at run-time, but is less precise, the latter can bring a costly overhead during execution, having to monitor any access to sensitive data and all destinations. Our approach is innovative in that it takes advantage of static analysis and then monitors at run-time only data paths that potentially give sensitive data out. The correspondent tool is tailored to Android environment, tool-chain, libraries, and typical requirements that applications have to satisfy.

SigSpot: mining significant anomalous regions from time-evolving networks (abstract only)

Anomaly detection in dynamic networks has a rich gamut of application domains, such as road networks, communication networks and water distribution networks. An anomalous event, such as a traffic accident, denial of service attack or a chemical spill, can cause a local shift from normal behavior in the network state that persists over an interval of time. Detecting such anomalous regions of network and time extent in large real-world networks is a challenging task. Existing anomaly detection techniques focus on either the time series associated with individual network edges or on global anomalies that affect the entire network. In order to detect anomalous regions, one needs to consider both the time and the affected network substructure jointly, which brings forth computational challenges due to the combinatorial nature of possible solutions. We propose the problem of mining all Significant Anomalous Regions (SAR) in time-evolving networks that asks for the discovery of connected temporal subgraphs comprised of edges that significantly deviate from normal in a persistent manner. We propose an optimal Baseline algorithm for the problem and an efficient approximation, called S IG S POT. Compared to Baseline, SIGSPOT is up to one order of magnitude faster in real data, while achieving less than 10% average relative error rate. In synthetic datasets it is more than 30 times faster than Baseline with 94% accuracy and solves efficiently large instances that are infeasible (more than 10 hours running time) for Baseline. We demonstrate the utility of SIGSPOT for inferring accidents on road networks and study its scalability when detecting anomalies in social, transportation and synthetic evolving networks, spanning up to 1GB.

Distributed randomized algorithms for low-support data mining

Data mining in distributed systems has been facilitated by using high-support association rules. Less attention has been paid to distributed low-support/high-correlation data mining. This has proved useful in several fields such as computational biology, wireless networks, web mining, security and rare events analysis in industrial plants. In this paper we present distributed versions of efficient algorithms for low-support/high-correlation data mining such as Min-Hashing, K-Min-Hashing and Locality-Sensitive-Hashing. Experimental results on real data concerning scalability, speed-up and network traffic are reported.