The importance of geo-spatial data in critical applications such as emergency response, transportation, agriculture etc., has prompted the adoption of recent GeoSPARQL standard in many RDF processing engines. In addition to large repositories of geo-spatial data -- e.g., LinkedGeoData, OpenStreetMap, etc. -- spatial data is also routinely found in automatically constructed knowledgebases such as Yago and WikiData. While there have been research efforts for efficient processing of spatial data in RDF SPARQL, very little effort has gone into building end-to-end systems that can holistically handle complex SPARQL queries along with spatial filters. In this paper, we present Streak, a RDF data management system that is designed to support a wide-range of queries with spatial filters including complex joins, top-k, higher-order relationships over spatially enriched databases. Streak introduces various novel features such as a careful identifier encoding strategy for spatial and non-spatial entities, the use of a semantics-aware Quad-tree index that allows for early-termination and a clever use of adaptive query processing with zero plan-switch cost. We show that Streak can scale to some of the largest publicly available semantic data resources such as Yago3 and LinkedGeoData which contain spatial entities and quantifiable predicates useful for result ranking. For experimental evaluations, we focus on top-k distance join queries and demonstrate that Streak outperforms popular spatial join algorithms as well as state of the art end-to-end systems like Virtuoso and PostgreSQL.
Hash-based Rank Join (HRJN) @cite_24 and Nested Loop Rank Join (NRJN) @cite_28 are two widely used top- @math join algorithms in the relational world. HRJN accesses objects from left (or right) side of join and joins them with tuples seen so-far from right (or left) side of join. All join results are fed to a priority queue, which outputs the results to the users if they are above threshold, thus producing results incrementally. Nested Loop Rank Join (NRJN) algorithm is similar to HRJN, except that it follows a nested loop join strategy instead of buffering join inputs. We do not compare with a general top- @math join algorithms, HRJN and NRJN, since such top- @math operators for such spatial workloads have been shown to perform poorly when compared to a block-based algorithm @cite_37 and instead compare with the state-of-the-art spatial top- @math algorithm.
@cite_24 @cite_37 @cite_28
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Ranking queries, also known as top-k queries, produce results that are ordered on some computed score. Typically, these queries involve joins, where users are usually interested only in the top-k join results. Top-k queries are dominant in many emerging applications, e.g., multimedia retrieval by content, Web databases, data mining, middlewares, and most information retrieval applications. Current relational query processors do not handle ranking queries efficiently, especially when joins are involved. In this paper, we address supporting top-k join queries in relational query processors. We introduce a new rank-join algorithm that makes use of the individual orders of its inputs to produce join results ordered on a user-specified scoring function. The idea is to rank the join results progressively during the join operation. We introduce two physical query operators based on variants of ripple join that implement the rank-join algorithm. The operators are nonblocking and can be integrated into pipelined execution plans. We also propose an efficient heuristic designed to optimize a top-k join query by choosing the best join order. We address several practical issues and optimization heuristics to integrate the new join operators in practical query processors. We implement the new operators inside a prototype database engine based on PREDATOR. The experimental evaluation of our approach compares recent algorithms for joining ranked inputs and shows superior performance. Join is an important database operation. As computer architectures evolve, the best join algorithm may change hand. This paper re-examines two popular join algorithms -- hash join and sort-merge join -- to determine if the latest computer architecture trends shift the tide that has favored hash join for many years. For a fair comparison, we implemented the most optimized parallel version of both algorithms on the latest Intel Core i7 platform. Both implementations scale well with the number of cores in the system and take advantages of latest processor features for performance. Our hash-based implementation achieves more than 100M tuples per second which is 17X faster than the best reported performance on CPUs and 8X faster than that reported for GPUs. Moreover, the performance of our hash join implementation is consistent over a wide range of input data sizes from 64K to 128M tuples and is not affected by data skew. We compare this implementation to our highly optimized sort-based implementation that achieves 47M to 80M tuples per second. We developed analytical models to study how both algorithms would scale with upcoming processor architecture trends. Our analysis projects that current architectural trends of wider SIMD, more cores, and smaller memory bandwidth per core imply better scalability potential for sort-merge join. Consequently, sort-merge join is likely to outperform hash join on upcoming chip multiprocessors. In summary, we offer multicore implementations of hash join and sort-merge join which consistently outperform all previously reported results. We further conclude that the tide that favors the hash join algorithm has not changed yet, but the change is just around the corner. Recently, Haas and Hellerstein proposed the hash ripple join algorithm in the context of online aggregation. Although the algorithm rapidly gives a good estimate for many join-aggregate problem instances, the convergence can be slow if the number of tuples that satisfy the join predicate is small or if there are many groups in the output. Furthermore, if memory overflows (for example, because the user allows the algorithm to run to completion for an exact answer), the algorithm degenerates to block ripple join and performance suffers. In this paper, we build on the work of Haas and Hellerstein and propose a new algorithm that (a) combines parallelism with sampling to speed convergence, and (b) maintains good performance in the presence of memory overflow. Results from a prototype implementation in a parallel DBMS show that its rate of convergence scales with the number of processors, and that when allowed to run to completion, even in the presence of memory overflow, it is competitive with the traditional parallel hybrid hash join algorithm. Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets.