@techreport{oai:ipsj.ixsq.nii.ac.jp:00106920,
 author = {Wolfgang, Mulzer and Yannik, Stein and Wolfgang, Mulzer and Yannik, Stein},
 issue = {28},
 month = {Nov},
 note = {Let P1,..., Pd+1 ⊂ Rd be point sets whose convex hulls each contain the origin. Each set represents a color class. The Colorful Caratheodory theorem guarantees the existence of a colorful choice, i.e., a set that contains exactly one point from each color class, whose convex hull also contains the origin. So far, the computational complexity of computing such a colorful choice is unknown and thus approximation algorithms are of interest. We consider a new notion of approximation: a set C′ is called an m-colorful choice if it contains at most m points from each color class. We show that for all constant ε > 0, an ε(d+1)-colorful choice containing the origin in its convex hull can be found in polynomial time., Let P1,..., Pd+1 ⊂ Rd be point sets whose convex hulls each contain the origin. Each set represents a color class. The Colorful Caratheodory theorem guarantees the existence of a colorful choice, i.e., a set that contains exactly one point from each color class, whose convex hull also contains the origin. So far, the computational complexity of computing such a colorful choice is unknown and thus approximation algorithms are of interest. We consider a new notion of approximation: a set C′ is called an m-colorful choice if it contains at most m points from each color class. We show that for all constant ε > 0, an ε(d+1)-colorful choice containing the origin in its convex hull can be found in polynomial time.},
 title = {Approximating the Colorful Caratheodory Theorem},
 year = {2014}
}