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COCOA
2010
Springer
13 years 2 months ago
The Union of Colorful Simplices Spanned by a Colored Point Set
A simplex spanned by a colored point set in Euclidean d-space is colorful if all vertices have distinct colors. The union of all full-dimensional colorful simplices spanned by a c...
André Schulz, Csaba D. Tóth
CCCG
2008
13 years 5 months ago
Monochromatic simplices of any volume
We give a very short proof of the following result of Graham from 1980: For any finite coloring of Rd , d 2, and for any > 0, there is a monochromatic (d + 1)-tuple that span...
Adrian Dumitrescu, Minghui Jiang
ESA
2001
Springer
104views Algorithms» more  ESA 2001»
13 years 8 months ago
Smallest Color-Spanning Objects
Motivated by questions in location planning, we show for a set of colored point sites in the plane how to compute the smallest— by perimeter or area—axis-parallel rectangle and...
Manuel Abellanas, Ferran Hurtado, Christian Icking...
SIAMDM
2010
123views more  SIAMDM 2010»
13 years 2 months ago
Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons
We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES (k) such that any set S of at least fES (k) points in general posit...
Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Fe...
COMPGEOM
2006
ACM
13 years 10 months ago
Colored intersection searching via sparse rectangular matrix multiplication
In a Batched Colored Intersection Searching Problem (CI), one is given a set of n geometric objects (of a certain class). Each object is colored by one of c colors, and the goal i...
Haim Kaplan, Micha Sharir, Elad Verbin