Abstract: An optimized method of processing queries requesting a description of a spatial relationship between a test geometry and a query geometry, such as points, lines, polygons, and collections thereof, is disclosed. A first part of the method finds a first spatial relationship between a minimum bounding rectangle (MBR) of the test geometry and an In-Memory R-tree (IMR-tree) built to describe the query geometry. If the first relationship does not specify the requested description, then a second part of the method uses the IMR-tree of the query geometry to find a second spatial relationship between the test geometry itself and the query geometry. Optimizations are applied to the first part and to the second part. Optimizations in the second part depend on the test geometry.

Abstract: Techniques are described for memory-efficient spatial histogram construction. A hierarchical spatial index has leaf nodes and non-leaf nodes, each leaf node representing a bounding region containing a spatial object, each non-leaf node representing a bounding region at least partially containing one or more spatial objects. A plurality of selected nodes is selected from the plurality of non-leaf nodes. The plurality of selected nodes includes an ancestor of each leaf node. For each particular node in the plurality of selected nodes, a weight is determined. The weight is based on the number of spatial objects contained within the bounding region of the particular node. A spatial partitioning of the plurality of selected nodes is determined. A spatial histogram is generated based on the spatial partitioning of the weights of the plurality of selected nodes.

Abstract: An optimized method of processing queries requesting a description of a spatial relationship between a test geometry and a query geometry, such as points, lines, polygons, and collections thereof, is disclosed. A first part of the method finds a first spatial relationship between a minimum bounding rectangle (MBR) of the test geometry and an In-Memory R-tree (IMR-tree) built to describe the query geometry. If the first relationship does not specify the requested description, then a second part of the method uses the IMR-tree of the query geometry to find a second spatial relationship between the test geometry itself and the query geometry. Optimizations are applied to the first part and to the second part. Optimizations in the second part depend on the test geometry.

Abstract: An optimized method of processing queries requesting a description of a spatial relationship between a test geometry and a query geometry, such as points, lines, polygons, and collections thereof, is disclosed. A first part of the method finds a first spatial relationship between a minimum bounding rectangle (MBR) of the test geometry and an In-Memory R-tree (IMR-tree) built to describe the query geometry. If the first relationship does not specify the requested description, then a second part of the method uses the IMR-tree of the query geometry to find a second spatial relationship between the test geometry itself and the query geometry. Optimizations are applied to the first part and to the second part. Optimizations in the second part depend on the test geometry.

Abstract: Techniques are described for memory-efficient spatial histogram construction. A hierarchical spatial index has leaf nodes and non-leaf nodes, each leaf node representing a bounding region containing a spatial object, each non-leaf node representing a bounding region at least partially containing one or more spatial objects. A plurality of selected nodes is selected from the plurality of non-leaf nodes. The plurality of selected nodes includes an ancestor of each leaf node. For each particular node in the plurality of selected nodes, a weight is determined. The weight is based on the number of spatial objects contained within the bounding region of the particular node. A spatial partitioning of the plurality of selected nodes is determined. A spatial histogram is generated based on the spatial partitioning of the weights of the plurality of selected nodes.

Abstract: An optimized method of processing queries requesting a description of a spatial relationship between a test geometry and a query geometry, such as points, lines, polygons, and collections thereof, is disclosed. A first part of the method finds a first spatial relationship between a minimum bounding rectangle (MBR) of the test geometry and an In-Memory R-tree (IMR-tree) built to describe the query geometry. If the first relationship does not specify the requested description, then a second part of the method uses the IMR-tree of the query geometry to find a second spatial relationship between the test geometry itself and the query geometry. Optimizations are applied to the first part and to the second part. Optimizations in the second part depend on the test geometry.

Abstract: Techniques are described for generating histograms for a multidimensional space. In the presence of large spatial objects, fuzzy splitting techniques are utilized to recursively divide the multidimensional space into partitions, where a single spatial object may belong to multiple partitions. Large spatial objects are essentially broken down into smaller objects that may allow for more efficient partitioning of the multidimensional space. A count of spatial objects in each partition yields a spatial histogram. A spatial object that belongs to multiple partitions may have a weighted count for each of the multiple partitions, based on the extent to which the spatial object overlaps with each partition. Thus, an object that is split among a handful of partitions will only contribute a fraction of a count to each partition. Small partitions having relatively few objects are avoided by refusing to subdivide a partition whose members drop below a threshold number.

Abstract: Techniques are described for generating histograms for a multidimensional space. In the presence of large spatial objects, fuzzy splitting techniques are utilized to recursively divide the multidimensional space into partitions, where a single spatial object may belong to multiple partitions. Large spatial objects are essentially broken down into smaller objects that may allow for more efficient partitioning of the multidimensional space. A count of spatial objects in each partition yields a spatial histogram. A spatial object that belongs to multiple partitions may have a weighted count for each of the multiple partitions, based on the extent to which the spatial object overlaps with each partition. Thus, an object that is split among a handful of partitions will only contribute a fraction of a count to each partition. Small partitions having relatively few objects are avoided by refusing to subdivide a partition whose members drop below a threshold number.

Abstract: A method for processing a first data stream specifying locations of a user at different times and a second data stream specifying values of a monitored attribute at a location of interest at different times includes: receiving a location-centric trigger specifying at least one spatial predicate condition relative to the location of interest and at least one non-spatial predicate condition relevant to the location of interest, calculating a safe region that includes locations whose probability of satisfying the spatial predicate condition falls below a first threshold, calculating a safe value container that includes values whose probability of satisfying the non-spatial predicate condition falls below a second threshold, and processing the first data stream and the second data stream against the location-centric trigger, by considering only those locations that are not contained within the safe region and only those values that are not contained within the safe value container.

Abstract: A method for processing a first data stream specifying locations of a user at different times and a second data stream specifying values of a monitored attribute at a location of interest at different times includes: receiving a location-centric trigger specifying at least one spatial predicate condition relative to the location of interest and at least one non-spatial predicate condition relevant to the location of interest, calculating a safe region that includes locations whose probability of satisfying the spatial predicate condition falls below a first threshold, calculating a safe value container that includes values whose probability of satisfying the non-spatial predicate condition falls below a second threshold, and processing the first data stream and the second data stream against the location-centric trigger, by considering only those locations that are not contained within the safe region and only those values that are not contained within the safe value container.

Abstract: A scalable, performance-based, volume allocation technique that can be applied in large storage controller collections is disclosed. A global resource tree of multiple nodes representing interconnected components of a storage system in a plurality of component layers is analyzed to yield gap values for each node (e.g., a bottom-up estimation). The gap value for each node is an estimate of the amount in GB of the new workload that can be allocated in the subtree of that node without exceeding the performance and space bounds at any of the nodes in that subtree. The gap values of the global resource tree are further analyzed to generate an ordered allocation list of the volumes of the storage system (e.g., a top-down selection). The volumes may be applied to a storage workload in the order of the allocation list and the gap values and list are updated.

Abstract: A storage placement planning system receives a resource graph describing SAN's resources and virtual machine applications requiring a particular amount of a processing resource element and a storage resource element. The system then determines a coupled placement of the processing element and storage element for each of the applications on a coupled pair of the resource nodes based on a specified throughput and a distance factor between coupled pairs of resource nodes. The coupled placement is determined using an algorithm that implements a cost function that determines affinities between processing nodes and storage nodes for each of said applications of a particular workload. The coupled placement for each of said applications identifies the particular amount of processing resource element placed on a first node for providing a processing resource and the particular amount of storage resource element placed on a second node for providing a storage resource for that application.

Abstract: A method for processing a first data stream specifying locations of a user at different times and a second data stream specifying values of a monitored attribute at a location of interest at different times includes: receiving a location-centric trigger specifying at least one spatial predicate condition relative to the location of interest and at least one non-spatial predicate condition relevant to the location of interest, calculating a safe region that includes locations whose probability of satisfying the spatial predicate condition falls below a first threshold, calculating a safe value container that includes values whose probability of satisfying the non-spatial predicate condition falls below a second threshold, and processing the first data stream and the second data stream against the location-centric trigger, by considering only those locations that are not contained within the safe region and only those values that are not contained within the safe value container.

Abstract: A method for processing a first data stream specifying locations of a user at different times and a second data stream specifying values of a monitored attribute at a location of interest at different times includes: receiving a location-centric trigger specifying at least one spatial predicate condition relative to the location of interest and at least one non-spatial predicate condition relevant to the location of interest, calculating a safe region that includes locations whose probability of satisfying the spatial predicate condition falls below a first threshold, calculating a safe value container that includes values whose probability of satisfying the non-spatial predicate condition falls below a second threshold, and processing the first data stream and the second data stream against the location-centric trigger, by considering only those locations that are not contained within the safe region and only those values that are not contained within the safe value container.

Abstract: A method for processing a first data stream specifying locations of a user at different times and a second data stream specifying values of a monitored attribute at a location of interest at different times includes: receiving a location-centric trigger specifying at least one spatial predicate condition relative to the location of interest and at least one non-spatial predicate condition relevant to the location of interest, calculating a safe region that includes locations whose probability of satisfying the spatial predicate condition falls below a first threshold, calculating a safe value container that includes values whose probability of satisfying the non-spatial predicate condition falls below a second threshold, and processing the first data stream and the second data stream against the location-centric trigger, by considering only those locations that are not contained within the safe region and only those values that are not contained within the safe value container.

Abstract: A scalable, performance-based, volume allocation technique that can be applied in large storage controller collections is disclosed. A global resource tree of multiple nodes representing interconnected components of a storage system in a plurality of component layers is analyzed to yield gap values for each node (e.g., a bottom-up estimation). The gap value for each node is an estimate of the amount in GB of the new workload that can be allocated in the subtree of that node without exceeding the performance and space bounds at any of the nodes in that subtree. The gap values of the global resource tree are further analyzed to generate an ordered allocation list of the volumes of the storage system (e.g., a top-down selection). The volumes may be applied to a storage workload in the order of the allocation list and the gap values and list are updated.

Abstract: A method for processing a first data stream specifying locations of a user at different times and a second data stream specifying values of a monitored attribute at a location of interest at different times includes: receiving a location-centric trigger specifying at least one spatial predicate condition relative to the location of interest and at least one non-spatial predicate condition relevant to the location of interest, calculating a safe region that includes locations whose probability of satisfying the spatial predicate condition falls below a first threshold, calculating a safe value container that includes values whose probability of satisfying the non-spatial predicate condition falls below a second threshold, and processing the first data stream and the second data stream against the location-centric trigger, by considering only those locations that are not contained within the safe region and only those values that are not contained within the safe value container.

Abstract: A scalable, performance-based, volume allocation technique that can be applied in large storage controller collections is disclosed. A global resource tree of multiple nodes representing interconnected components of a storage system is analyzed to yield gap values for each node (e.g., a bottom-up estimation). The gap value for each node is an estimate of the amount in GB of the new workload that can be allocated in the subtree of that node without exceeding the performance and space bounds at any of the nodes in that subtree. The gap values of the global resource tree are further analyzed to generate an ordered allocation list of the volumes of the storage system (e.g., a top-down selection). The volumes may be applied to a storage workload in the order of the allocation list and the gap values and list are updated.

Abstract: The importance of semantic web resources is determined. Some resources are classes (of the type RDFS:Class); others are non-class resources. Non-class resources belong to one or more classes while class resources are subclasses of one or more parent classes. A subjectivity score is determined for each resource of a set of resources based on the number of Resource Description Format (RDF) triples of which the resource is the subject and predefined weights of properties of the triples. An objectivity score is determined for each resource based on the number of RDF triples of which the resource is the object and predefined weights of the properties of the triples. The importance of a class is determined from the respective subjectivity score and objectivity score, and a factor relating to the importance of the class's parents.

Abstract: A program, method and system are disclosed for planning the placement of a collection of applications in a heterogeneous storage area network data center. The program, method, and system disclosed deal with the coupled placement of virtual machine applications within a resource graph, with each application requiring a certain amount of CPU resources and a certain amount of storage resources from the connected resource node pairs within the resource graph. The resource nodes in the graph provide either storage resources, CPU resources, or both and can have differing degrees of affinity between different node pairs. Various placement algorithms may be used to optimize placement of the applications such as an individual-greedy, pair-greedy or stable marriage algorithm. One placement objective may be to place the programs among nodes of the resource graph without exceeding the storage and CPU capacities at nodes while keeping the total cost over all applications small.