Intersection and Decomposition Algorithms for Planar Arrangements . By Pankaj K. Agarwal. Cambridge University Press, Cambridge, 1991 . xvii+277 pp . $39 .50 cloth . ISBN 0-521-40446-0 . This book encapsulates perfectly the primary concerns and methods in the field of Computational Geometry at the start of the 1990's . It illustrates, as well as any piece of work, the deep and beautiful connections between combinatorics, geometry, and efficient algorithms . The book is a (light) revision of Agarwal ' s 1989 NYU PhD thesis, supervised by Micha . Sharir . Like most theses, it focuses on the new contributions and the technical difficulties i n achieving them . There is less history, context, and consequences than a research monograp h might offer . Nevertheless, within the thesis-writing genre, and given the technical nature of the topic, the writing is remarkably clear . `The book contains four major theoretical contributions, and a host of related result s and applications . The first result (joint work with Sharir and Peter Shor) r establishes ne w bounds on the complexity of Davenport-Schinzel sequences . Atallah was the first to notic e their relevance to computational geometry, and Sharir was the
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Book Review: Intersection and Decomposition Algorithms for Planar Arrangements, by Pankaj K. Agarwal. (Cambridge University Press, Cambridge, 1991 . xvii+277 pp . $39.50 cloth. ISBN 0-521-40446-0)
Reviewer-O'Rourke, Joseph
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