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posted on 01.01.1975by Michael I. Shamos
The complexity of a number of fundamental problems in computational geometry is examined and a number
of new fast algorithms are presented and analyzed. General methods for obtaining results in geometric
complexity are given and upper and lower bounds are obtained for problems involving sets of points, lines,
and polygons in the plane. An effort is made to recast classical theorems into a useful computational form
and analogies are developed between constructibility questions in Euclidean geometry and computability
questions in modern computational complexity.