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84
ClosureTree: An Index Structure for Graph Queries
, 2006
"... Graphs have become popular for modeling structured data. As a result, graph queries are becoming common and graph indexing has come to play an essential role in query processing. We introduce the concept of a graph closure, a generalized graph that represents a number of graphs. Our indexing techniq ..."
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Cited by 88 (1 self)
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Graphs have become popular for modeling structured data. As a result, graph queries are becoming common and graph indexing has come to play an essential role in query processing. We introduce the concept of a graph closure, a generalized graph that represents a number of graphs. Our indexing technique, called Closuretree, organizes graphs hierarchically where each node summarizes its descendants by a graph closure. Closuretree can efficiently support both subgraph queries and similarity queries. Subgraph queries find graphs that contain a specific subgraph, whereas similarity queries find graphs that are similar to a query graph. For subgraph queries, we propose a technique called pseudo subgraph isomorphism which approximates subgraph isomorphism with high accuracy. For similarity queries, we measure graph similarity through edit distance using heuristic graph mapping methods. We implement two kinds of similarity queries: KNN query and range query. Our experiments on chemical compounds and synthetic graphs show that for subgraph queries, Closuretree outperforms existing techniques by up to two orders of magnitude in terms of candidate answer set size and index size. For similarity queries, our experiments validate the quality and efficiency of the presented algorithms.
Treepi: A novel graph indexing method
 in Proc. of ICDE
, 2007
"... Graphs are widely used to model complex structured data such as XML documents, protein networks, and chemical compounds. One of the fundamental problems in graph databases is efficient search and retrieval of graphs using indexing techniques. In this paper, we study the problem of indexing graph da ..."
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Cited by 52 (2 self)
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Graphs are widely used to model complex structured data such as XML documents, protein networks, and chemical compounds. One of the fundamental problems in graph databases is efficient search and retrieval of graphs using indexing techniques. In this paper, we study the problem of indexing graph databases using frequent subtrees as indexing structures. Trees can be manipulated efficiently while preserving a lot of structural information of the original graphs. In our proposed method, frequent subtrees of a database are selected as the feature set. To save memory, the set of feature trees is shrunk based on a support threshold function and their discriminative power. A treepartition based query processing scheme is proposed to perform graph queries. The concept of Center Distance Constraints is introduced to prune the search space. Furthermore, a new algorithm which utilizes the location information of indexing structures is used to perform subgraph isomorphism tests. We apply our method on a wide range of real and synthetic data to demonstrate the usefulness and effectiveness of this approach. 1
LargeScale Malware Indexing Using FunctionCall Graphs
"... A major challenge of the antivirus (AV) industry is how to effectively process the huge influx of malware samples they receive every day. One possible solution to this problem is to quickly determine if a new malware sample is similar to any previouslyseen malware program. In this paper, we design ..."
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Cited by 51 (0 self)
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A major challenge of the antivirus (AV) industry is how to effectively process the huge influx of malware samples they receive every day. One possible solution to this problem is to quickly determine if a new malware sample is similar to any previouslyseen malware program. In this paper, we design, implement and evaluate a malware database management system called SMIT (Symantec Malware Indexing Tree) that can efficiently make such determination based on malware’s functioncall graphs, which is a structural representation known to be less susceptible to instructionlevel obfuscations commonly employed by malware writers to evade detection of AV software. Because each malware program is represented as a graph, the problem of searching for the most similar malware program in a database to a given malware sample is cast into a nearestneighbor search problem in a graph database. To speed
Taming Verification Hardness: An Efficient Algorithm for Testing Subgraph Isomorphism
"... Graphs are widely used to model complicated data semantics in many applications. In this paper, we aim to develop efficient techniques to retrieve graphs, containing a given query graph, from a large set of graphs. Considering the problem of testing subgraph isomorphism is generally NPhard, most of ..."
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Cited by 47 (8 self)
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Graphs are widely used to model complicated data semantics in many applications. In this paper, we aim to develop efficient techniques to retrieve graphs, containing a given query graph, from a large set of graphs. Considering the problem of testing subgraph isomorphism is generally NPhard, most of the existing techniques are based on the framework of filteringandverification to reduce the precise computation costs; consequently various novel featurebased indexes have been developed. While the existing techniques work well for small query graphs, the verification phase becomes a bottleneck when the query graph size increases. Motivated by this, in the paper we firstly propose a novel and efficient algorithm for testing subgraph isomorphism, QuickSI. Secondly, we develop a new featurebased index technique to accommodate QuickSI in the filtering phase. Our extensive experiments on real and synthetic data demonstrate the efficiency and scalability of the proposed techniques, which significantly improve the existing techniques. 1.
Gstring: A novel approach for efficient search in graph databases
 In ICDE
, 2007
"... Graphs are widely used for modeling complicated data, including chemical compounds, protein interactions, XML documents, and multimedia. Information retrieval against such data can be formulated as a graph search problem, and finding an efficient solution to the problem is essential for many applica ..."
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Cited by 42 (5 self)
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Graphs are widely used for modeling complicated data, including chemical compounds, protein interactions, XML documents, and multimedia. Information retrieval against such data can be formulated as a graph search problem, and finding an efficient solution to the problem is essential for many applications. A popular approach is to represent both graphs and queries on graphs by sequences, thus converting graph search to subsequence matching. Stateoftheart sequencing methods work at the finest granularity – each node (or edge) in the graph will appear as an element in the resulting sequence. Clearly, such methods are not semantic conscious, and the resulting sequences are not only bulky but also prone to complexities arising from graph isomorphism and other problems in searching. In this paper, we introduce a novel sequencing method to capture the semantics of the underlying graph data. We find meaningful components in graph structures and use them as the most basic units in sequencing. It not only reduces the size of resulting sequences, but also enables semanticbased searching. In this paper, we base our approach on chemical compound databases, although it can be applied to searching other complicated graphs, such as protein structures. Experiments demonstrate that our approach outperforms stateoftheart graph search methods. 1.
Less is more: Compact matrix decomposition for large sparse graphs
, 2007
"... Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and regulatory networks in genes. Low rank decompositions, such as ..."
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Cited by 34 (3 self)
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Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and regulatory networks in genes. Low rank decompositions, such as SVD and CUR, are powerful techniques for revealing latent/hidden variables and associated patterns from high dimensional data. However, those methods often ignore the sparsity property of the graph, and hence usually incur too high memory and computational cost to be practical. We propose a novel method, the Compact Matrix Decomposition (CMD), to compute sparse low rank approximations. CMD dramatically reduces both the computation cost and the space requirements over existing decomposition methods (SVD, CUR). Using CMD as the key building block, we further propose procedures to efficiently construct and analyze dynamic graphs from realtime application data. We provide theoretical guarantee for our methods, and present results on two real, large datasets, one on network flow data (100GB trace of 22K hosts over one month) and one on DBLP (200MB over 25 years). We show that CMD is often an order of magnitude more efficient than the state of the art (SVD and CUR): it is over 10X faster, but requires less than 1/10 of the space, for the same reconstruction accuracy. Finally, we demonstrate how CMD is used for detecting anomalies and monitoring timeevolving graphs, in which it successfully detects wormlike hierarchical scanning patterns in real network data.
Efficient subgraph matching on billion node graphs
 In PVLDB
, 2012
"... The ability to handle large scale graph data is crucial to an increasing number of applications. Much work has been dedicated to supporting basic graph operations such as subgraph matching, reachability, regular expression matching, etc. In many cases, graph indices are employed to speed up query pr ..."
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Cited by 30 (5 self)
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The ability to handle large scale graph data is crucial to an increasing number of applications. Much work has been dedicated to supporting basic graph operations such as subgraph matching, reachability, regular expression matching, etc. In many cases, graph indices are employed to speed up query processing. Typically, most indices require either superlinear indexing time or superlinear indexing space. Unfortunately, for very large graphs, superlinear approaches are almost always infeasible. In this paper, we study the problem of subgraph matching on billionnode graphs. We present a novel algorithm that supports efficient subgraph matching for graphs deployed on a distributed memory store. Instead of relying on superlinear indices, we use efficient graph exploration and massive parallel computing for query processing. Our experimental results demonstrate the feasibility of performing subgraph matching on webscale graph data. 1.
A Survey of Frequent Subgraph Mining Algorithms
 THE KNOWLEDGE ENGINEERING REVIEW
, 2004
"... Graph mining is an important research area within the domain of data mining. The field of study concentrates on the identification of frequent subgraphs within graph data sets. The research goals are directed at: (i) effective mechanisms for generating candidate subgraphs (without generating duplica ..."
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Cited by 27 (1 self)
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Graph mining is an important research area within the domain of data mining. The field of study concentrates on the identification of frequent subgraphs within graph data sets. The research goals are directed at: (i) effective mechanisms for generating candidate subgraphs (without generating duplicates) and (ii) how best to process the generated candidate subgraphs so as to identify the desired frequent subgraphs in a way that is computationally efficient and procedurally effective. This paper presents a survey of current research in the field of frequent subgraph mining, and proposed solutions to address the main research issues.
Fast computation of simrank for static and dynamic information networks
 IN: EDBT
, 2010
"... Information networks are ubiquitous in many applications and analysis on such networks has attracted significant attention in the academic communities. One of the most important aspects of information network analysis is to measure similarity between nodes in a network. SimRank is a simple and influ ..."
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Cited by 26 (1 self)
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Information networks are ubiquitous in many applications and analysis on such networks has attracted significant attention in the academic communities. One of the most important aspects of information network analysis is to measure similarity between nodes in a network. SimRank is a simple and influential measure of this kind, based on a solid theoretical “random surfer ” model. Existing work computes SimRank similarity scores in an iterative mode. We argue that the iterative method can be infeasible and inefficient when, as in many realworld scenarios, the networks change dynamically and frequently. We envision noniterative method to bridge the gap. It allows users not only to update the similarity scores incrementally, but also to derive similarity scores for an arbitrary subset of nodes. To enable the noniterative computation, we propose to rewrite the SimRank equation into a noniterative form by using the Kronecker product and vectorization operators. Based on this, we develop a family of novel approximate SimRank computation algorithms for static and dynamic information networks, and give their corresponding theoretical justification and analysis. The noniterative method supports efficient processing of various node analysis including similarity tracking and centrality tracking on evolving information networks. The effectiveness and efficiency of our proposed methods are evaluated on synthetic and real data sets.