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Algorithms in Combinatorial Geometry (Paperback, Softcover reprint of the original 1st ed. 1987)
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Algorithms in Combinatorial Geometry (Paperback, Softcover reprint of the original 1st ed. 1987)
Series: Monographs in Theoretical Computer Science. An EATCS Series, 10
Expected to ship within 18 - 22 working days
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Computational geometry as an area of research in its own right
emerged in the early seventies of this century. Right from the
beginning, it was obvious that strong connections of various kinds
exist to questions studied in the considerably older field of
combinatorial geometry. For example, the combinatorial structure of
a geometric problem usually decides which algorithmic method solves
the problem most efficiently. Furthermore, the analysis of an
algorithm often requires a great deal of combinatorial knowledge.
As it turns out, however, the connection between the two research
areas commonly referred to as computa tional geometry and
combinatorial geometry is not as lop-sided as it appears. Indeed,
the interest in computational issues in geometry gives a new and
con structive direction to the combinatorial study of geometry. It
is the intention of this book to demonstrate that computational and
com binatorial investigations in geometry are doomed to profit from
each other. To reach this goal, I designed this book to consist of
three parts, acorn binatorial part, a computational part, and one
that presents applications of the results of the first two parts.
The choice of the topics covered in this book was guided by my
attempt to describe the most fundamental algorithms in
computational geometry that have an interesting combinatorial
structure. In this early stage geometric transforms played an
important role as they reveal connections between seemingly
unrelated problems and thus help to structure the field."
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