44 citations · 279 across the 33 of their papers we have counts for
5 papers · 1 filter
Reachability by Paths of Bounded Curvature in a Convex Polygon
Hee-Kap Ahn, Otfried Cheong, Jirí Matoušek +1
Let be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let be a convex polygon with vertices. Given a st…
A geometric proof of the colored Tverberg theorem
Jiří Matoušek, Martin Tancer, Uli Wagner
The colored Tverberg theorem asserts that for every d and r there exists t=t(d,r) such that for every set C in R^d of cardinality (d+1)t, partitioned into t-point subsets C_1,C_2,.…
The number of unit distances is almost linear for most norms
Jiří Matoušek
We prove that there exists a norm in the plane under which no n-point set determines more than O(n log n log log n) unit distances. Actually, most norms have this property, in the…
On the nonexistence of k-reptile tetrahedra
Jiří Matoušek, Zuzana Safernová
A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S_1,S_2,...,S_k that are all congruent and similar to S. For d=2, k-reptile simplic…
Minimum and maximum against k lies
Michael Hoffmann, Jiří Matoušek, Yoshio Okamoto +1
A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element tota…