Range Searching in Categorical Data: Colored Range Searching on Grid
نویسندگان
چکیده
Range searching, a fundamental problem in numerous applications areas, has been widely studied in computational geometry and spatial databases. Given a set of geometric objects, a typical range query asks for reporting all the objects that intersect a query object. However in many applications, including databases and network routing, input objects are partitioned into categories and a query asks for reporting the set of categories of objects that intersect a query object. Moreover in many such applications, objects lie on a grid. We abstract the category of an object by associating a color with each object. In this paper, we present efficient data structures for solving the colored range-searching and colored point-enclosure problem on U U grid. Our data structures use nearlinear space and answer a query in O(log logU + k) time, where k is the output size. As far as we know, this is the first result on colored range-searching for objects lying on a grid.
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