Eliminating Duplicates under Interval and Fuzzy Uncertainty: An Asymptotically Optimal Algorithm and Its Geospatial Applications

Geospatial databases generally consist of measurements related to points (or pixels in the case of raster data), lines, and polygons. In recent years, the size and complexity of these databases have increased signiicantly and they often contain duplicate records, i.e., two or more close records representing the same measurement result. In this paper, we address the problem of detecting duplicates in a database consisting of point measurements. As a test case, we use a database of measurements of anomalies in the Earth's gravity eld that we have compiled. In this paper, we show that a natural duplicate deletion algorithm requires (in the worst case) quadratic time, and we propose a new asymptotically optimal O(n log(n)) algorithm. These algorithms have been successfully applied to gravity databases. We believe that they will prove to be useful when dealing with many other types of point data. Geospatial databases: general description. In many application areas, researchers and practitioners have collected a large amount of geospatial data. 1 For example, geophysicists measure values d of the gravity and magnetic elds, elevation, and reeectivity of electromagnetic energy for a broad range of wavelengths (visible, infrared, and radar) at diierent geographical points (x; y); see, e.g., 35]. Each type of data is usually stored in a large geospatial database that contains corresponding records (x i ; y i ; d i). Based on these measurements, geophysicists generate maps and images and derive geophysical models that t these measurements. Gravity measurements: case study. In particular, gravity measurements are one of the most important sources of information about subsurface structure and physical conditions. There are two reasons for this importance. First, in contrast to more widely used geophysical data like remote sensing images, that mainly reeect the conditions of the Earth's surface, gravitation comes from the whole Earth (e.g., 19, 20]). Thus gravity data contain valuable information about much deeper geophysical structures. Second, in contrast to many types of geophysical data, which usually cover a reasonably local area, gravity measurements cover broad areas and thus provide important regional information. The accumulated gravity measurement data are stored at several research centers around the world. One of these data storage centers is located at the University of Texas at El Paso (UTEP). This center contains gravity measurements collected throughout the United States and Mexico and parts of Africa. The geophysical use of gravity database compiled at UTEP is illustrated for Duplicates: …