text: Given a query graph that represents a pattern of interest, the emerging pattern detection problem can be viewed as a continuous query problem on a dynamic graph. We present an incremental algorithm for continuous query processing on dynamic graphs. The algorithm is based on the concept of query decomposition; we decompose a query graph into smaller subgraphs and assemble the result of sub-queries to find complete matches with the specified query. The novelty of our work lies in using the subgraph distributional statistics collected from the dynamic graph to generate the decomposition. We introduce a "Lazy Search" algorithm where the search strategy is decided on a vertex-to-vertex basis depending on the likelihood of a match in the vertex neighborhood. We also propose a metric named "Relative Selectivity" that is used to select between different query decomposition strategies. Our experiments performed on real online news, network traffic stream and a synthetic social network benchmark demonstrate 10-100x speedups over competing approaches.
  @cite_14: Large graph datasets are common in many emerging database applications, and most notably in large-scale scientific applications. To fully exploit the wealth of information encoded in graphs, effective and efficient graph matching tools are critical. Due to the noisy and incomplete nature of real graph datasets, approximate, rather than exact, graph matching is required. Furthermore, many modern applications need to query large graphs, each of which has hundreds to thousands of nodes and edges. This paper presents a novel technique for approximate matching of large graph queries. We propose a novel indexing method that incorporates graph structural information in a hybrid index structure. This indexing technique achieves high pruning power and the index size scales linearly with the database size. In addition, we propose an innovative matching paradigm to query large graphs. This technique distinguishes nodes by their importance in the graph structure. The matching algorithm first matches the important nodes of a query and then progressively extends these matches. Through experiments on several real datasets, this paper demonstrates the effectiveness and efficiency of the proposed method.
  @cite_4: 
  @cite_7: We present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs. A first version of the algorithm has been presented in a previous paper, where we examined its performance for the isomorphism of small and medium size graphs. The algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs; its features are analyzed in detail with special reference to time and memory requirements. The results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented, confirming the effectiveness of the approach, especially when working with large graphs.
  @cite_0: 
  @cite_23: Many dynamic applications are built upon large network infrastructures, such as social networks, communication networks, biological networks and the Web. Such applications create data that can be naturally modeled as graph streams, in which edges of the underlying graph are received and updated sequentially in a form of a stream. It is often necessary and important to summarize the behavior of graph streams in order to enable effective query processing. However, the sheer size and dynamic nature of graph streams present an enormous challenge to existing graph management techniques. In this paper, we propose a new graph sketch method, gSketch, which combines well studied synopses for traditional data streams with a sketch partitioning technique, to estimate and optimize the responses to basic queries on graph streams. We consider two different scenarios for query estimation: (1) A graph stream sample is available; (2) Both a graph stream sample and a query workload sample are available. Algorithms for different scenarios are designed respectively by partitioning a global sketch to a group of localized sketches in order to optimize the query estimation accuracy. We perform extensive experimental studies on both real and synthetic data sets and demonstrate the power and robustness of gSketch in comparison with the state-of-the-art global sketch method.
  @cite_15: Given a query graph q and a data graph g, the subgraph isomorphism search finds all occurrences of q in g and is considered one of the most fundamental query types for many real applications. While this problem belongs to NP-hard, many algorithms have been proposed to solve it in a reasonable time for real datasets. However, a recent study has shown, through an extensive benchmark with various real datasets, that all existing algorithms have serious problems in their matching order selection. Furthermore, all algorithms blindly permutate all possible mappings for query vertices, often leading to useless computations. In this paper, we present an efficient and robust subgraph search solution, called TurboISO, which is turbo-charged with two novel concepts, candidate region exploration and the combine and permute strategy (in short, Comb Perm). The candidate region exploration identifies on-the-fly candidate subgraphs (i.e, candidate regions), which contain embeddings, and computes a robust matching order for each candidate region explored. The Comb Perm strategy exploits the novel concept of the neighborhood equivalence class (NEC). Each query vertex in the same NEC has identically matching data vertices. During subgraph isomorphism search, Comb Perm generates only combinations for each NEC instead of permutating all possible enumerations. Thus, if a chosen combination is determined to not contribute to a complete solution, all possible permutations for that combination will be safely pruned. Extensive experiments with many real datasets show that TurboISO consistently and significantly outperforms all competitors by up to several orders of magnitude.
  @cite_16: Complex social and information network search becomes important with a variety of applications. In the core of these applications, lies a common and critical problem: Given a labeled network and a query graph, how to efficiently search the query graph in the target network. The presence of noise and the incomplete knowledge about the structure and content of the target network make it unrealistic to find an exact match. Rather, it is more appealing to find the top-k approximate matches. In this paper, we propose a neighborhood-based similarity measure that could avoid costly graph isomorphism and edit distance computation. Under this new measure, we prove that subgraph similarity search is NP hard, while graph similarity match is polynomial. By studying the principles behind this measure, we found an information propagation model that is able to convert a large network into a set of multidimensional vectors, where sophisticated indexing and similarity search algorithms are available. The proposed method, called Ness (Neighborhood Based Similarity Search), is appropriate for graphs with low automorphism and high noise, which are common in many social and information networks. Ness is not only efficient, but also robust against structural noise and information loss. Empirical results show that it can quickly and accurately find high-quality matches in large networks, with negligible cost.
  @cite_13: Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph isomorphism, clique detection, graph isomorphism, and directed graph isomorphism experiments have been carried out with random and with various nonrandom graphs. A parallel asynchronous logic-in-memory implementation of a vital part of the algorithm is also described, although this hardware has not actually been built. The hardware implementation would allow very rapid determination of isomorphism.
  @cite_11: A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graph-based techniques in the Pattern Recognition and Machine Vision field.
summary: Graph querying techniques have been studied extensively in the field of pattern recognition over nearly four decades @cite_11 . Two popular subgraph isomorphism algorithms were developed by Ullman @cite_13 and @cite_7 . The VF2 algorithm @cite_7 employs a filtering and verification strategy and outperforms the original algorithm by Ullman. Over the past decade, the database community has focused strongly on developing indexing and query optimization techniques to speed up the searching process. A common theme of such approaches is to index vertices based on k-hop neighborhood signatures derived from labels and other properties such as degrees and centrality @cite_14 @cite_4 @cite_0 . Other major areas of work involve exploration of subgraph equivalence classes @cite_15 and search techniques for alternative representations such as similarity search in a multi-dimensional vector space @cite_16 . Apart from neighborhood based signatures, is an important area that focuses on generating different synopses of a graph data set @cite_23 . Development of efficient graph sketching algorithms and their applications into query estimation is expected to gain prominence in the near future.