No Arabic abstract
Single-source and top-$k$ SimRank queries are two important types of similarity search in graphs with numerous applications in web mining, social network analysis, spam detection, etc. A plethora of techniques have been proposed for these two types of queries, but very few can efficiently support similarity search over large dynamic graphs, due to either significant preprocessing time or large space overheads. This paper presents ProbeSim, an index-free algorithm for single-source and top-$k$ SimRank queries that provides a non-trivial theoretical guarantee in the absolute error of query results. ProbeSim estimates SimRank similarities without precomputing any indexing structures, and thus can naturally support real-time SimRank queries on dynamic graphs. Besides the theoretical guarantee, ProbeSim also offers satisfying practical efficiency and effectiveness due to several non-trivial optimizations. We conduct extensive experiments on a number of benchmark datasets, which demonstrate that our solutions significantly outperform the existing methods in terms of efficiency and effectiveness. Notably, our experiments include the first empirical study that evaluates the effectiveness of SimRank algorithms on graphs with billion edges, using the idea of pooling.
Facility location queries identify the best locations to set up new facilities for providing service to its users. Majority of the existing works in this space assume that the user locations are static. Such limitations are too restrictive for planning many modern real-life services such as fuel stations, ATMs, convenience stores, cellphone base-stations, etc. that are widely accessed by mobile users. The placement of such services should, therefore, factor in the mobility patterns or trajectories of the users rather than simply their static locations. In this work, we introduce the TOPS (Trajectory-Aware Optimal Placement of Services) query that locates the best k sites on a road network. The aim is to optimize a wide class of objective functions defined over the user trajectories. We show that the problem is NP-hard and even the greedy heuristic with an approximation bound of (1-1/e) fails to scale on urban-scale datasets. To overcome this challenge, we develop a multi-resolution clustering based indexing framework called NetClus. Empirical studies on real road network trajectory datasets show that NetClus offers solutions that are comparable in terms of quality with those of the greedy heuristic, while having practical response times and low memory footprints. Additionally, the NetClus framework can absorb dynamic updates in mobility patterns, handle constraints such as site-costs and capacity, and existing services, thereby providing an effective solution for modern urban-scale scenarios.
Top-k query processing finds a list of k results that have largest scores w.r.t the user given query, with the assumption that all the k results are independent to each other. In practice, some of the top-k results returned can be very similar to each other. As a result some of the top-k results returned are redundant. In the literature, diversified top-k search has been studied to return k results that take both score and diversity into consideration. Most existing solutions on diversified top-k search assume that scores of all the search results are given, and some works solve the diversity problem on a specific problem and can hardly be extended to general cases. In this paper, we study the diversified top-k search problem. We define a general diversified top-k search problem that only considers the similarity of the search results themselves. We propose a framework, such that most existing solutions for top-k query processing can be extended easily to handle diversified top-k search, by simply applying three new functions, a sufficient stop condition sufficient(), a necessary stop condition necessary(), and an algorithm for diversified top-k search on the current set of generated results, div-search-current(). We propose three new algorithms, namely, div-astar, div-dp, and div-cut to solve the div-search-current() problem. div-astar is an A* based algorithm, div-dp is an algorithm that decomposes the results into components which are searched using div-astar independently and combined using dynamic programming. div-cut further decomposes the current set of generated results using cut points and combines the results using sophisticated operations. We conducted extensive performance studies using two real datasets, enwiki and reuters. Our div-cut algorithm finds the optimal solution for diversified top-k search problem in seconds even for k as large as 2,000.
Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary queries over probabilistic databases with arbitrary dependencies expressed by graphical models with structure that changes during inference. MCMC sampling provides efficiency by hypothesizing {em modifications} to possible worlds rather than generating entire worlds from scratch. Queries are then run over the portions of the world that change, avoiding the onerous cost of running full queries over each sampled world. A significant innovation of this work is the connection between MCMC sampling and materialized view maintenance techniques: we find empirically that using view maintenance techniques is several orders of magnitude faster than naively querying each sampled world. We also demonstrate our systems ability to answer relational queries with aggregation, and demonstrate additional scalability through the use of parallelization.
Betweenness centrality, measured by the number of times a vertex occurs on all shortest paths of a graph, has been recognized as a key indicator for the importance of a vertex in the network. However, the betweenness of a vertex is often very hard to compute because it needs to explore all the shortest paths between the other vertices. Recently, a relaxed concept called ego-betweenness was introduced which focuses on computing the betweenness of a vertex in its ego network. In this work, we study a problem of finding the top-k vertices with the highest ego-betweennesses. We first develop two novel search algorithms equipped with a basic upper bound and a dynamic upper bound to efficiently solve this problem. Then, we propose local-update and lazy-update solutions to maintain the ego-betweennesses for all vertices and the top-k results when the graph is updated, respectively. In addition, we also present two efficient parallel algorithms to further improve the efficiency. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.
Reachability query is a fundamental problem on graphs, which has been extensively studied in academia and industry. Since graphs are subject to frequent updates in many applications, it is essential to support efficient graph updates while offering good performance in reachability queries. Existing solutions compress the original graph with the Directed Acyclic Graph (DAG) and propose efficient query processing and index update techniques. However, they focus on optimizing the scenarios where the Strong Connected Components(SCCs) remain unchanged and have overlooked the prohibitively high cost of the DAG maintenance when SCCs are updated. In this paper, we propose DBL, an efficient DAG-free index to support the reachability query on dynamic graphs with insertion-only updates. DBL builds on two complementary indexes: Dynamic Landmark (DL) label and Bidirectional Leaf (BL) label. The former leverages landmark nodes to quickly determine reachable pairs whereas the latter prunes unreachable pairs by indexing the leaf nodes in the graph. We evaluate DBL against the state-of-the-art approaches on dynamic reachability index with extensive experiments on real-world datasets. The results have demonstrated that DBL achieves orders of magnitude speedup in terms of index update, while still producing competitive query efficiency.