Minimum-weight triangulation is NP-hard
- Wolfgang Mulzer, G. Rote
- Computer ScienceJACM
- 2 January 2006
It is proved that the decision version of the minimum-weight triangulation (MWT) problem is NP-hard, using a reduction from PLANAR 1-IN-3-SAT.
The convergence rate of the sandwich algorithm for approximating convex functions
- G. Rote
- Mathematics, Computer ScienceComputing
- 1 March 1992
The Sandwich algorithm approximates a convex function of one variable over an interval by evaluating the function and its derivative at a sequence of points and it is shown that the global approximation error withn evaluation points decreases by the order ofO(1/n2), which is optimal.
Incremental constructions con BRIO
- N. Amenta, Sunghee Choi, G. Rote
- Computer ScienceSCG '03
- 8 June 2003
A biased randomized insertion order is defined which removes enough randomness to significantly improve performance, but leaves enough Randomness so that the algorithms remain theoretically optimal.
Matching planar maps
Computing the Minimum Hausdorff Distance Between Two Point Sets on a Line Under Translation
- G. Rote
- Computer Science, MathematicsInformation Processing Letters
- 17 May 1991
Minimum-link paths among obstacles in the plane
- Joseph S. B. Mitchell, G. Rote, G. Woeginger
- Physics, MathematicsSCG '90
- 1 May 1990
An algorithm is presented that computes the link distance (and a corresponding minimum-link path) between two points in time using the extremely slowly growing inverse of Ackermann's function.
Simple and optimal output-sensitive construction of contour trees using monotone paths
- Yi-Jen Chiang, Tobias Lenz, Xiang Lu, G. Rote
- Computer ScienceComputational geometry
- 1 February 2005
Matching shapes with a reference point
- O. Aichholzer, H. Alt, G. Rote
- MathematicsSCG '94
- 10 June 1994
The focus of the paper is the general study of reference points (like the Steiner point) and their properties with respect to shape matching and a very simple algorithm to translate one set so that the Hausdorff distance between the two sets is not larger than a constant factor times the minimum Hausdorf distance.
Sequences With Subword Complexity 2n
- G. Rote
- 1 February 1994
Abstract We construct and discuss infinite 0-1-sequences which contain 2 n different sub-words of length n , for every n .
Computing the geodesic center of a simple polygon
- R. Pollack, M. Sharir, G. Rote
- Computer Science, MathematicsDiscrete & Computational Geometry
- 21 August 2011
An algorithm is presented which calculates the geodesic center of a simple polygon withn vertices in timeO(n logn) which minimizes the maximum internal distance to any point in the polygon.