Efficient Range Query Using Multiple Hilbert Curves

Abstract

Indoor location tracking based on RFID has been widely discussed and applied. RFID reading process is efficient and reliable, therefore it is suitable for discovering locations inside buildings where GPS signals are usually unreachable. In general, there are two approaches for location sensing using RFID. 1) Deploying RFID tags at fixed locations and RFID readers attached to moving objects (Willis, 2004). Each tag represents a reference point in the space, and a reader determines its location by the set of tags being detected. 2) Deploying RFID readers (and tags) at fixed locations and RDIF tags attached to moving objects (Hightower, 2001; Ni, 2004). The readers report to the system when a tag is detected, and the system identifies the location of this tag by the set of readers that have reported and their corresponding signal strength. These location management systems require multi-dimensional access methods to allow efficient handling of spatial queries. Because there is no total ordering of locations that preserves the spatial locality between objects, it is difficult to design multi-dimensional access method in the way as traditional one-dimensional access methods. However, mapping multi-dimensional data into a single dimension makes it possible to utilize the extensively exploited B/B+-tree as the index and its associated concurrency control and recovery mechanisms. Space-filling curves (SFCs) (Simmons, 1963) have been widely used to map the multidimensional data points into a linear order. It was first introduced by Peano (Peano, 1890) to map from a unit interval to a unit square. SFC can link all cells with passing through each of them only once, so it provides a way of generating a total linear ordering of all grids in a multi-dimensional space. Many SFCs have been proposed in the literature, such as Peano curve (or Z-order) (Orenstein & Merrett, 1984; Peano, 1890), Hilbert curve (Hilbert, 1891), Gray curve (Gray, 1953), Sweep, and Scan. The multi-dimensional data are transformed to a set of one-dimensional integer values using SFC mapping schemes. The transformed data can be stored in a traditional one-dimensional database based on the linear orders, and indexed by B-trees or B+-trees. Then the spatial queries, such as range query, kNN query, and spatial join, can be processed. Using SFCs to enable processing spatial queries based on traditional one-dimensional indices is proposed in (Faloutsos, 1988; Faloutsos & Rong, 1991; Faloutsos & Roseman, 1989; Jagadish, 1990).