Several geometric problems can be formulated in terms of the
arrangement of a collection of curves in a plane, which has made
this one of the most widely studied topics in computational
geometry. This book, first published in 1991, presents a study of
various problems related to arrangements of lines, segments, or
curves in the plane. The first problem is a proof of almost tight
bounds on the length of (n,s)-Davenport-Schinzel sequences, a
technique for obtaining optimal bounds for numerous algorithmic
problems. Then the intersection problem is treated. The final
problem is improving the efficiency of partitioning algorithms,
particularly those used to construct spanning trees with low
stabbing numbers, a very versatile tool in solving geometric
problems. A number of applications are also discussed. Researchers
in computational and combinatorial geometry should find much to
interest them in this book.
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