Geometric Range Searching and Its Relatives
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چکیده
About ten years ago, the eld of range searching, especially simplex range searching, was wide open. At that time, neither e cient algorithms nor nontrivial lower bounds were known for most range-searching problems. A series of papers by Haussler and Welzl [161], Clarkson [88, 89], and Clarkson and Shor [92] not only marked the beginning of a new chapter in geometric searching, but also revitalized computational geometry as a whole. Led by these and a number of subsequent papers, tremendous progress has been made in geometric range searching, both in terms of developing e cient data structures and proving nontrivial lower bounds. From a theoretical point of view, range searching is now almost completely solved. The impact of general techniques developed for geometric range searching | "-nets, 1=rcuttings, partition trees, multi-level data structures, to name a few | is evident throughout computational geometry. This volume provides an excellent opportunity to recapitulate the current status of geometric range searching and to summarize the recent progress in this area. Range searching arises in a wide range of applications, including geographic information systems, computer graphics, spatial databases, and time-series databases. Furthermore, a variety of geometric problems can be formulated as a range-searching problem. A typical range-searching problem has the following form. Let S be a set of n points in R , and let
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تاریخ انتشار 1997