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he last few years have seen the emergence of a new generation of distributed systems that scale over the Internet, operate under decentralized settings, and are dynamic in their behavior (participants can leave or join the system). One such system is referred to as grid computing; other similar systems include peer-to-peer (P2P) computing [1], semantic Web [2], pervasive computing [3], and mobile computing [4, 5]. Grid computing [6] provides the basic infrastructure required for sharing diverse sets of resources, including desktops, computational clusters, supercomputers, storage, data, sensors, applications, and online scientific instruments. Grid computing offers its vast computational power to solve grand challenge problems in science and engineering such as protein folding, high energy physics, financial modeling, earthquake simulation, climate/weather modeling, aircraft engine diagnostics, earthquake engineering, virtual observatory, bioinformatics, drug discovery, digital image analysis, astrophysics, and multi-player gaming. Grids can primarily be classified [7] into various types, depending on the nature of their emphasis: computation, data, application service, interaction, knowledge, and utility. Accordingly, grids are proposed as the emerging cyber infrastructure to power utility computing applications. Computational grids aggregate the computational power of globally distributed computers (e.g., TeraGrid, ChinaGrid, and APAC-Grid). Data grids emphasize global-scale management of data to provide data access, integration, and processing through distributed data repositories (e.g., LHCGrid, Gri-PhyN). Application service (provisioning) grids focus on providing access to remote applications and modules; libraries hosted on data centers or computational grids (e.g., NetSolve and Grid-Solve). Interaction grids focus on interaction and collaborative visualization between participants (e.g., AccessGrid). Knowledge grids aim toward knowledge acquisition, processing, and management, and provide business analytics services driven by integrated data mining services. Utility grids focus on providing all the grid services, including compute power, data, and service to end users as IT utilities on a subscription basis, and provide the infrastructure necessary for negotiation of required quality of service, establishment and management of contracts, and allocation of resources to meet competing demands. To summarize, these grids follow a layered design IEEE Communications Surveys & Tutorials • 2nd Quarter 2008 6

Nowadays large amounts of GPS trajectory data is being continuously collected by GPS-enabled devices such as vehicles navigation systems and mobile phones. GPS trajectory data is useful for applications such as traffic management, location forecasting, and itinerary planning. Such applications often need to extract the time-stamped Sequence of Visited Locations (SVLs) of the mobile objects. The nearest neighbor query (NNQ) is the most applied method for labeling the visited locations based on the IDs of the POIs in the process of SVL generation. NNQ in some scenarios is not accurate enough. To improve the quality of the extracted SVLs, instead of using NNQ, we label the visited locations as the IDs of the POIs which geometrically intersect with the GPS observations. Intersection operator requires the accurate geometry of the points of interest which we refer to them as the Geometries