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.
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.
@cite_14 @cite_4 @cite_7 @cite_0 @cite_23 @cite_15 @cite_16 @cite_13 @cite_11
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In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection. In this paper, we study the problem of subgraph matching that extracts all subgraph isomorphic embeddings of a query graph q in a large data graph G. The existing algorithms for subgraph matching follow Ullmann's backtracking approach; that is, iteratively map query vertices to data vertices by following a matching order of query vertices. It has been shown that the matching order of query vertices is a very important aspect to the efficiency of a subgraph matching algorithm. Recently, many advanced techniques, such as enforcing connectivity and merging similar vertices in query or data graphs, have been proposed to provide an effective matching order with the aim to reduce unpromising intermediate results especially the ones caused by redundant Cartesian products. In this paper, for the first time we address the issue of unpromising results by Cartesian products from "dissimilar" vertices. We propose a new framework by postponing the Cartesian products based on the structure of a query to minimize the redundant Cartesian products. Our second contribution is proposing a new path-based auxiliary data structure, with the size O(|E(G)| x |V(q)|), to generate a matching order and conduct subgraph matching, which significantly reduces the exponential size O(|V(G)||V(q)|-1) of the existing path-based auxiliary data structure, where V (G) and E (G) are the vertex and edge sets of a data graph G, respectively, and V (q) is the vertex set of a query @math . Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms by up to @math orders of magnitude. The growing popularity of graph databases has generated interesting data management problems, such as subgraph search, shortest-path query, reachability verification, and pattern match. Among these, a pattern match query is more flexible compared to a subgraph search and more informative compared to a shortest-path or reachability query. In this paper, we address pattern match problems over a large data graph G. Specifically, given a pattern graph (i.e., query Q), we want to find all matches (in G) that have the similar connections as those in Q. In order to reduce the search space significantly, we first transform the vertices into points in a vector space via graph embedding techniques, coverting a pattern match query into a distance-based multi-way join problem over the converted vector space. We also propose several pruning strategies and a join order selection method to process join processing efficiently. Extensive experiments on both real and synthetic datasets show that our method outperforms existing ones by orders of magnitude. Subgraph querying has been applied in a variety of emerging applications. Traditional subgraph querying based on subgraph isomorphism requires identical label matching, which is often too restrictive to capture the matches that are semantically close to the query graphs. This paper extends subgraph querying to identify semantically related matches by leveraging ontology information. (1) We introduce the ontology-based subgraph querying, which revises subgraph isomorphism by mapping a query to semantically related subgraphs in terms of a given ontology graph. We introduce a metric to measure the similarity of the matches. Based on the metric, we introduce an optimization problem to find top K best matches. (2) We provide a filtering-and-verification framework to identify (top-K) matches for ontology-based subgraph queries. The framework efficiently extracts a small subgraph of the data graph from an ontology index, and further computes the matches by only accessing the extracted subgraph. (3) In addition, we show that the ontology index can be efficiently updated upon the changes to the data graphs, enabling the framework to cope with dynamic data graphs. (4) We experimentally verify the effectiveness and efficiency of our framework using both synthetic and real life graphs, comparing with traditional subgraph querying methods.