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SimRank is a powerful model for assessing vertex-pair similarities in a graph. It follows the concept that two vertices are similar if they are referenced by similar vertices. The prior work [18] exploits partial sums memoization to compute SimRank in O(Kmn) time on a graph of n vertices and m edges, for K iterations. However, computations among different partial sums may have redundancy. Besides, to guarantee a given accuracy \epsilon , the existing SimRank needs K=\lceil \log _C \,\epsilon \rceil time, where d^{\prime } is typically much smaller than \frac{m}{n} . (2) A new differential SimRank equation is proposed, which can represent the SimRank matrix as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) In bipartite domains, a novel finer-grained partial max clustering method is developed to speed up the computation of the Minimax SimRank variation from O(Kmn) to O(Km^{\prime }n) time, where m^{\prime } \ ({\le} m)$ is the number of edges in a reduced graph after edge clustering, which can be typically much smaller than $m$ . Using real and synthetic data, we empirically verify that (1) our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude; (2) the revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores; (3) our finer-grained partial max memoization for the Minimax SimRank variation in bipartite domains is 5X-12X faster than the baselines. [ABSTRACT FROM PUBLISHER]

SimRank is a widely adopted similarity measure for objects modeled as nodes in a graph, based on the intuition that two objects are similar if they are referenced by similar objects. The recursive nature of SimRank definition makes it expensive to compute the similarity score even for a single pair of nodes. This defect limits the applications of SimRank. To speed up the computation, some existing works replace the original model with an approximate model to seek only rough solution of SimRank scores. In this work, we propose a novel solution for computing all-pair SimRank scores. In particular, we propose to convert SimRank to the problem of solving a linear system in matrix form, and further prove that the system is non-singular, diagonally dominate, and symmetric definite positive (for undirected graphs). Those features immediately lead to the adoption of Conjugate Gradient (CG) and Bi-Conjugate Gradient (BiCG) techniques for efficiently computing SimRank scores. As a result, a significant improvement on the convergence rate can be achieved; meanwhile, the sparsity of the adjacency matrix is not damaged all the time. Inspired by the existing common neighbor sharing strategy, we further reduce the computational complexity of the matrix multiplication and resolve the scalable issues. The experimental results show our proposed algorithms significantly outperform the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Core decomposition is a fundamental graph problem with a large number of applications. Most existing approaches for core decomposition assume that the graph is kept in memory of a machine. Nevertheless, many real-world graphs are too big to reside in memory. In this paper, we study I/O efficient core decomposition following a semi-external model, which only allows node information to be loaded in memory. We propose a semi-external algorithm and an optimized algorithm for I/O efficient core decomposition. To handle dynamic graph updates, we firstly show that our algorithm can be naturally extended to handle edge deletion. Then, we propose an I/O efficient core maintenance algorithm to handle edge insertion, and an improved algorithm to further reduce I/O and CPU cost. In addition, based on our core decomposition algorithms, we further propose an I/O efficient semi-external algorithm for degeneracy ordering, which is an important graph problem that is highly related to core decomposition. We also consider how to maintain the degeneracy order. We conduct extensive experiments on 12 real large graphs. Our optimal core decomposition algorithm significantly outperforms the existing I/O efficient algorithm in terms of both processing time and memory consumption. They are very scalable to handle web-scale graphs. As an example, we are the first to handle a web graph with 978.5 million nodes and 42.6 billion edges using less than 4.2 GB memory. We also show that our proposed algorithms for degeneracy order computation and maintenance can handle big graphs efficiently with small memory overhead. [ABSTRACT FROM AUTHOR]

Given a social network \mathcal G and a positive integer $k$ , the influence maximization problem aims to identify a set of $k$ nodes in \mathcal G that can maximize the influence spread under a certain propagation model. As the proliferation of geo-social networks, location-aware promotion is becoming more necessary in real applications. In this paper, we study the distance-aware influence maximization (DAIM) problem, which advocates the importance of the distance between users and the promoted location. Unlike the traditional influence maximization problem, DAIM treats users differently based on their distances from the promoted location. In this situation, the $k$ nodes selected are different when the promoted location varies. In order to handle the large number of queries and meet the online requirement, we develop two novel index-based approaches, MIA-DA and RIS-DA, by utilizing the information over some pre-sampled query locations. MIA-DA is a heuristic method which adopts the maximum influence arborescence (MIA) model to approximate the influence calculation. In addition, different pruning strategies as well as a priority-based algorithm are proposed to significantly reduce the searching space. To improve the effectiveness, in RIS-DA, we extend the reverse influence sampling (RIS) model and come up with an unbiased estimator for the DAIM problem. Through carefully analyzing the sample size needed for indexing, RIS-DA is able to return a $1 - 1/e -\epsilon$ approximate solution with at least $1 - \delta$ probability for any given query. Finally, we demonstrate the efficiency and effectiveness of proposed methods over real geo-social networks. [ABSTRACT FROM PUBLISHER]

Due to a variety of reasons including data randomness and incompleteness, noise, privacy, etc., uncertainty is inherent in many important applications, such as location-based services (LBS), sensor network monitoring, and radio-frequency identification (RFID). Recently, considerable research efforts have been devoted into the field of uncertainty-aware spatial query processing such that the uncertainty of the data can be effectively and efficiently tackled. In this paper, we study the problem of finding top $k$ most influential facilities over a set of uncertain objects, which is an important and fundamental spatial query in the above applications. Based on the maximal utility principle, we propose a new ranking model to identify the top $k$ most influential facilities, which carefully captures influence of facilities on the uncertain objects. By utilizing two uncertain object indexing techniques, $R$ -tree and $U$ -Quadtree, effective and efficient algorithms are proposed following the filtering and verification paradigm, which significantly improves the performance of the algorithms in terms of CPU and I/O costs. To effectively support uncertain objects with a large number of instances, we also develop randomized algorithms with accuracy guarantee. Then, a hybrid algorithm is devised which effectively combines the randomized and exact algorithms. Comprehensive experiments on real datasets demonstrate the effectiveness and efficiency of our techniques. [ABSTRACT FROM PUBLISHER]

Given a positive value r, a distance-based range query returns the objects that lie within the distance r of the query location. In this paper, we focus on the distance-based range queries that continuously change their locations in a euclidean space. We present an efficient and effective monitoring technique based on the concept of a safe zone. The safe zone of a query is the area with a property that while the query remains inside it, the results of the query remain unchanged. Hence, the query does not need to be reevaluated unless it leaves the safe zone. Our contributions are as follows: 1) We propose a technique based on powerful pruning rules and a unique access order which efficiently computes the safe zone and minimizes the I/O cost. 2) We theoretically determine and experimentally verify the expected distance a query moves before leaving the safe zone and, for majority of queries, the expected number of guard objects. 3) Our experiments demonstrate that the proposed approach is close to optimal and is an order of magnitude faster than a naïve algorithm. 4) We also extend our technique to monitor the queries in a road network. Our algorithm is up to two order of magnitude faster than a naïve algorithm. [ABSTRACT FROM AUTHOR]