10,435 research outputs found
Approximating the Maximum Overlap of Polygons under Translation
Let and be two simple polygons in the plane of total complexity ,
each of which can be decomposed into at most convex parts. We present an
-approximation algorithm, for finding the translation of ,
which maximizes its area of overlap with . Our algorithm runs in
time, where is a constant that depends only on and .
This suggest that for polygons that are "close" to being convex, the problem
can be solved (approximately), in near linear time
Algebras related to posets of hyperplanes
We compare two noncommutative algebras which are related to arrangements of hyperplanes. For three special arrangements the induced approximately finite dimensional -algebra and the graded Orlik-Solomon-algebra are investigated
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