The Lock-free kk-LSM Relaxed Priority Queue

Priority queues are data structures which store keys in an ordered fashion to allow efficient access to the minimal (maximal) key. Priority queues are essential for many applications, e.g., Dijkstra's single-source shortest path algorithm, branch-and-bound algorithms, and prioritized schedulers. Efficient multiprocessor computing requires implementations of basic data structures that can be used concurrently and scale to large numbers of threads and cores. Lock-free data structures promise superior scalability by avoiding blocking synchronization primitives, but the \emph{delete-min} operation is an inherent scalability bottleneck in concurrent priority queues. Recent work has focused on alleviating this obstacle either by batching operations, or by relaxing the requirements to the \emph{delete-min} operation. We present a new, lock-free priority queue that relaxes the \emph{delete-min} operation so that it is allowed to delete \emph{any} of the $\rho+1$ smallest keys, where $\rho$ is a runtime configurable parameter. Additionally, the behavior is identical to a non-relaxed priority queue for items added and removed by the same thread. The priority queue is built from a logarithmic number of sorted arrays in a way similar to log-structured merge-trees. We experimentally compare our priority queue to recent state-of-the-art lock-free priority queues, both with relaxed and non-relaxed semantics, showing high performance and good scalability of our approach.Comment: Short version as ACM PPoPP'15 poste

Fast and Accurate Random Walk with Restart on Dynamic Graphs with Guarantees

Given a time-evolving graph, how can we track similarity between nodes in a fast and accurate way, with theoretical guarantees on the convergence and the error? Random Walk with Restart (RWR) is a popular measure to estimate the similarity between nodes and has been exploited in numerous applications. Many real-world graphs are dynamic with frequent insertion/deletion of edges; thus, tracking RWR scores on dynamic graphs in an efficient way has aroused much interest among data mining researchers. Recently, dynamic RWR models based on the propagation of scores across a given graph have been proposed, and have succeeded in outperforming previous other approaches to compute RWR dynamically. However, those models fail to guarantee exactness and convergence time for updating RWR in a generalized form. In this paper, we propose OSP, a fast and accurate algorithm for computing dynamic RWR with insertion/deletion of nodes/edges in a directed/undirected graph. When the graph is updated, OSP first calculates offset scores around the modified edges, propagates the offset scores across the updated graph, and then merges them with the current RWR scores to get updated RWR scores. We prove the exactness of OSP and introduce OSP-T, a version of OSP which regulates a trade-off between accuracy and computation time by using error tolerance {\epsilon}. Given restart probability c, OSP-T guarantees to return RWR scores with O ({\epsilon} /c ) error in O (log ({\epsilon}/2)/log(1-c)) iterations. Through extensive experiments, we show that OSP tracks RWR exactly up to 4605x faster than existing static RWR method on dynamic graphs, and OSP-T requires up to 15x less time with 730x lower L1 norm error and 3.3x lower rank error than other state-of-the-art dynamic RWR methods.Comment: 10 pages, 8 figure

DESQ: Frequent Sequence Mining with Subsequence Constraints

Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and hierarchy constraints. In this paper, we show that many subsequence constraints---including and beyond those considered in the literature---can be unified in a single framework. A unified treatment allows researchers to study jointly many types of subsequence constraints (instead of each one individually) and helps to improve usability of pattern mining systems for practitioners. In more detail, we propose a set of simple and intuitive "pattern expressions" to describe subsequence constraints and explore algorithms for efficiently mining frequent subsequences under such general constraints. Our algorithms translate pattern expressions to compressed finite state transducers, which we use as computational model, and simulate these transducers in a way suitable for frequent sequence mining. Our experimental study on real-world datasets indicates that our algorithms---although more general---are competitive to existing state-of-the-art algorithms.Comment: Long version of the paper accepted at the IEEE ICDM 2016 conferenc