منابع مشابه
On pseudo-convex decompositions, partitions, and coverings
We introduce pseudo-convex decompositions, partitions, and coverings for planar point sets. They are natural extensions of their convex counterparts and use both convex polygons and pseudo-triangles. We discuss some of their basic combinatorial properties and establish upper and lower bounds on their complexity.
متن کاملDecompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles
We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their c...
متن کاملConvex Decompositions
We consider decompositions S of a closed, convex set P into smaller, closed and convex regions. The thin convex decompositions are those having a certain strong convexity property as a set of sets. Thin convexity is directly connected to our intended application in voting theory (see [8, 9]), via the consistency property for abstract voting systems. The facial decompositions are those for which...
متن کاملMinimal Convex Decompositions
Let P be a set of n points on the plane in general position. We say that a set Γ of convex polygons with vertices in P is a convex decomposition of P if: Union of all elements in Γ is the convex hull of P, every element in Γ is empty, and for any two different elements of Γ their interiors are disjoint. A minimal convex decomposition of P is a convex decomposition Γ′ such that for any two adjac...
متن کاملCubical Convex Ear Decompositions
We consider the problem of constructing a convex ear decomposition for a poset. The usual technique, introduced by Nyman and Swartz, starts with a CL-labeling and uses this to shell the ‘ears’ of the decomposition. We axiomatize the necessary conditions for this technique as a “CL-ced” or “EL-ced”. We find an EL-ced of the d-divisible partition lattice, and a closely related convex ear decompos...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1979
ISSN: 0022-247X
DOI: 10.1016/0022-247x(79)90039-8