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In contrast to queries for on-line transaction processing (OLTP) systems that typically access only a small portion of a database, OLAP queries may need to aggregate large portions of a database which often leads to performance issues. In this paper we introduce CR-OLAP, a scalable Cloud based Real-time OLAP system based on a new distributed index structure for OLAP, the distributed PDCR tree. CR-OLAP utilizes a scalable cloud infrastructure consisting of multiple commodity servers (processors). That is, with increasing database size, CR-OLAP dynamically increases the number of processors to maintain performance. Our distributed PDCR tree data structure supports multiple dimension hierarchies and efficient query processing on the elaborate dimension hierarchies which are so central to OLAP systems. It is particularly efficient for complex OLAP queries that need to aggregate large portions of the data warehouse, such as "report the total sales in all stores located in California and New York during the months February-May of all years". We evaluated CR-OLAP on the Amazon EC2 cloud, using the TPC-DS benchmark data set. The tests demonstrate that CR-OLAP scales well with increasing number of processors, even for complex queries. For example, for an Amazon EC2 cloud instance with 16 processors, a data warehouse with 160 million tuples, and a TPC-DS OLAP query stream where each query aggregates between 60% and 95% of the database, CR-OLAP achieved a query latency of below 0.3 s which can be considered a real time response. Collaboration with the IBM on alleviating performance bottlenecks for OLAP queries.OLAP queries may aggregate large portions of the database, creating bottlenecks.We study the use of parallel computing on scalable clouds to accelerate queries.Our system, CR-OLAP, is based on a new scalable distributed index structure.CR-OLAP uses dynamic cloud elasticity to improve performance.

We present a parallel algorithm for solving thenext element search problemon a set of line segments, using a BSP-like model referred to as thecoarse grained multicomputer(CGM). The algorithm requiresO(1) communication rounds (h-relations withh=O(n/p)),O((n/p)logn) local computation, andO((n/p)logp) memory per processor, assumingn/p?p. Our result implies solutions to the point location, trapezoidal decomposition, and polygon triangulation problems. A simplified version for axis-parallel segments requires onlyO(n/p) memory per processor, and we discuss an implementation of this version. As in a previous paper by Develliers and Fabri (Int. J. Comput. Geom. Appl.6(1996), 487?506), our algorithm is based on a distributed implementation of segment trees which are of sizeO(nlogn). This paper improves onop. cit.in several ways: (1) It studies the more general next element search problem which also solves, e.g., planar point location. (2) The algorithms require onlyO((n/p)logn) local computation instead ofO(logp*(n/p)logn). (3) The algorithms require onlyO((n/p)logp) local memory instead ofO((n/p)logn).

We present a parallel algorithm for the construction of the hyperoctree representing a d-dimensional object from a set of n (d ? 1)-dimensional hyperoctrees, representing adjacent cross sections of this object. On a p-processor SIMD hypercube the time complexity of our algorithm is O((m/p) log p log n), where m is the maximum of input and output size.

The multisearch problem is defined as follows. Given a data structure D modeled as a graph with n constant-degree nodes, perform O(n) searches on D. Let r be the length of the longest search path associated with a search process, and assume that the paths are determined "on-line." That is, the search paths may overlap arbitrarily. In this paper, we solve the multisearch problem for certain classes of graphs in O([formula] + r ([formula]/log n)) time on a [formula] × [formula]n mesh-connected computer. For many data structures, the search path traversed when answering one search query has length r = O(log n). For these cases, our algorithm processes O(n) such queries in asymptotically optimal Θ([formula]) time. The classes of graphs we consider contain many of the important data structures that arise in practice, ranging from simple trees to Kirkpatrick hierarchical search DAGs. Multisearch is a useful abstraction that can be used to implement parallel versions of standard sequential data structures on a mesh. As example applications, we consider a variety of parallel on-line tree traversals, as well as hierarchical representations of polyhedra and its myriad of applications (line-polyhedron intersection queries, multiple tangent plane determination, intersecting convex polyhedra, and three-dimensional convex hull).

Given a rectangle R (with its edges parallel to the coordinate axes) containing a set S = { s 1 ,…, s n } of n points in the Euclidean plane, consider the problem of finding the largest area subrectangle r in R with sides parallel to the coordinate axes that contains no point of S . We present optimal parallel algorithms for solving this problem on one- and two-dimensional arrays of processors.