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CCCG
1996
13 years 9 months ago
Generalizing Halfspaces
Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restri...
Eugene Fink, Derick Wood
JCO
2008
153views more  JCO 2008»
13 years 7 months ago
A quadratic lower bound for colourful simplicial depth
We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in Rd is contained in at least (d + 2)2 /4 simplices with one vertex from each set.
Tamon Stephen, Hugh Thomas
GC
2007
Springer
13 years 7 months ago
Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-Triangles
We propose a novel subdivision of the plane that consists of both convex polygons and pseudotriangles. This pseudo-convex decomposition is significantly sparser than either conve...
Oswin Aichholzer, Clemens Huemer, S. Kappes, Betti...
STOC
1993
ACM
76views Algorithms» more  STOC 1993»
13 years 11 months ago
Piecewise linear paths among convex obstacles
Let B be a set of n arbitrary possibly intersecting convex obstacles in Rd. It is shown that any two points which can be connected by a path avoiding the obstacles can also be c...
Mark de Berg, Jirí Matousek, Otfried Schwar...
CORR
2008
Springer
92views Education» more  CORR 2008»
13 years 7 months ago
Convex Sparse Matrix Factorizations
We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by...
Francis Bach, Julien Mairal, Jean Ponce