Simplex Range Searching and Its Variants: A Review



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 \(\mathbb{R}^{d}\), and let \(\mathbb{R}\) be a family of subsets of \(\mathbb{R}^{d}\); elements of \(\mathbb{R}\) are called ranges. Preprocess S into a data structure so that for a query range \(\gamma \in \mathbb{R}\), the points in Sγ can be reported or counted efficiently. Notwithstanding extensive work on range searching over the last four decades, it remains an active research area. A series of papers by Jirka Matoušek and others in the late 1980s and the early 1990s had a profound impact not only on range searching but also on computational geometry as a whole. This chapter reviews the known results and techniques, including recent developments, for simplex range searching and its variants.


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Authors and Affiliations

  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA

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