Digitale Medien
Springer
Discrete & computational geometry
4 (1989), S. 139-181
ISSN:
1432-0444
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Informatik
,
Mathematik
Notizen:
Abstract This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF02187720
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