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 $q$. Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms by up to $3$ orders of magnitude.

It is widely realized that the integration of database and information retrieval techniques will provide users with a wide range of high quality services. In this paper, we study processing an l-keyword query, p ₁ , p ₁ , ..., p _l , against a relational database which can be modeled as a weighted graph, G(V, E). Here V is a set of nodes (tuples) and E is a set of edges representing foreign key references between tuples. Let V _i ⊆ V be a set of nodes that contain the keyword p _i . We study finding top-k minimum cost connected trees that contain at least one node in every subset V _i , and denote our problem as GST-k When k = 1, it is known as a minimum cost group Steiner tree problem which is NP-complete. We observe that the number of keywords, l, is small, and propose a novel parameterized solution, with l as a parameter, to find the optimal GST-1, in time complexity O(3 ^l n + 2 ^l ((l + logn)n + m)), where n and m are the numbers of nodes and edges in graph G. Our solution can handle graphs with a large number of nodes. Our GST-1 solution can be easily extended to support GST-k, which outperforms the existing GST-k solutions over both weighted undirected/directed graphs. We conducted extensive experimental studies, and report our finding.

Community search is a problem of finding densely connected subgraphs that satisfy the query conditions in a network, which has attracted much attention in recent years. However, all the previous studies on community search do not consider the influence of a community. In this paper, we introduce a novel community model called k -influential community based on the concept of k -core, which can capture the influence of a community. Based on the new community model, we propose a linear-time online search algorithm to find the top- r k -influential communities in a network. To further speed up the influential community search algorithm, we devise a linear-space index structure which supports efficient search of the top- r k -influential communities in optimal time. We also propose an efficient algorithm to maintain the index when the network is frequently updated. We conduct extensive experiments on 7 real-world large networks, and the results demonstrate the efficiency and effectiveness of the proposed methods.

Community search is important in graph analysis and can be used in many applications. In the literature, various community models have been proposed. However, most of them cannot well identify the overlaps between communities which is an essential feature of real graphs. To address this issue, $k$-clique percolation community model was proposed and has been proven effective in many applications. Motivated by this, in this paper, we adopt the $k$-clique percolation community model and study the densest clique percolation community search problem which aims to find the $k$-clique percolation community with the maximum k value that contains a given set of query nodes. We adopt an index-based approach to solve this problem. Based on the observation that a $k$-clique percolation community is a union of maximal cliques, we devise a compact index, DCPC-Index, to preserve the maximal cliques and their connectivity information of the input graph. With DCPC-Index, we can answer the densest clique percolation community query efficiently. Besides, we also propose an index construction algorithm based on the definition of DCPC-Index and further improve the algorithm in terms of efficiency and memory consumption. The experimental results demonstrate the efficiency of our index-based query processing algorithm and index construction algorithm.