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Pankaj Kumar Agarwal is an Indian computer scientist and mathematician researching algorithms in computational geometry and related areas. He is the RJR Nabisco Professor of Computer Science and Mathematics at Duke University, where he has been chair of the computer science department since 2004.〔.〕 He obtained his Ph.D. in Computer Science in 1989 from the Courant Institute, New York, under the supervision of Micha Sharir.〔.〕 ==Books== Agarwal is the author or co-author of: *''Intersection and Decomposition Algorithms for Planar Arrangements'' (Cambridge University Press, 1991, ISBN 978-0-521-40446-4). The topics of this book are algorithms for and the combinatorial geometry of arrangements of lines and arrangements of more general types of curves in the Euclidean plane and the real projective plane. The topics covered in this monograph include Davenport–Schinzel sequences and their application to the complexity of single cells in arrangements, levels in arrangements, algorithms for building arrangements in part or in whole, and ray shooting in arrangements.〔Review of ''Intersection and Decomposition Algorithms for Planar Arrangements'' by Franz Aurenhammer, 1992, .〕 *''Davenport–Schinzel Sequences and their Geometric Applications'' (with Micha Sharir, Cambridge University Press, 1995, ISBN 978-0-521-47025-4). This book concerns Davenport–Schinzel sequences, sequences of symbols drawn from a given alphabet with the property that no subsequence of more than some finite length consists of two alternating symbols. As the book discusses, these sequences and combinatorial bounds on their length have many applications in combinatorial and computational geometry, including bounds on lower envelopes of sets of functions, single cells in arrangements, shortest paths, and dynamically-changing geometric structures.〔Review of ''Davenport–Schinzel Sequences and their Geometric Applications'' by Igor Rivin, 1996, .〕 *''Combinatorial Geometry'' (with János Pach, Wiley, 1995, ISBN 978-0-471-58890-0). This book, less specialized than the previous two, is split into two sections. The first, on packing and covering problems, includes topics such as Minkowski's theorem, sphere packing, the representation of planar graphs by tangent circles, the planar separator theorem. The second section, although primarily concerning arrangements, also includes topics from extremal graph theory, Vapnik–Chervonenkis dimension, and discrepancy theory.〔Review of ''Combinatorial Geometry'' by Martin Henk, 1996, .〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pankaj K. Agarwal」の詳細全文を読む スポンサード リンク
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