Geometric Range Searching and Its Relatives Geometric Range Searching and Its Relatives
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Geometric Range Searching and Its Relatives
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 revitali...
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A central problem in computational geometry, range searching arises in many applications, and numerous geometric problems can be formulated in terms of range searching. A typical range-searching problem has the following form. Let S be a set of n points in Rd, and let R be a family of subsets of Rd; elements of R are called ranges. Preprocess S into a data structure so that for a query range γ ...
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