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- Rolf Klein
- Lecture Notes in Computer Science
- 1989

We present a new class of curves which are self-approaching in the following sense. For any three consecutive points a, b, c on the curve the point b is closer to c than a to c. This is a generalisation of curves with increasing chords which are self-approaching in both directions. We show a tight upper bound of 5.3331. .. for the length of a… (More)

- Christian Icking, Rolf Klein, Lihong Ma
- CCCG
- 1993

- Christian Icking, Rolf Klein
- Int. J. Comput. Geometry Appl.
- 1991

Given a simple polygon in the plane with two distinguished vertices, s and g, is it possible for two guards to simultaneously walk along the two boundary chains from s to g in such a way that they are always mutually visible? We decide this question in time O(n log n) and in linear space, where n is the number of edges of the polygon. Moreover, we compute a… (More)

- Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel
- SIAM J. Comput.
- 2001

We present an on-line strategy that enables a mobile robot with vision to explore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest watchman tour that could be computed off-line. Our analysis is doubly founded on a novel geometric structure called the angle hull. Let D be a connected region inside a… (More)

- Rolf Klein, Martin Kutz
- Graph Drawing
- 2006

We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if edge crossings are allowed or forbidden. We also show that the problem remains NP-hard even when a minimum-dilation tour or path is sought; not even an FPTAS exists in this case.

- Rolf Klein
- Comput. Geom.
- 1991

A polygon with two distinguished vertices, s and g, is called a street iff the two boundary chains from s t o g are mutually weakly visible. For a mobile robot with on-board vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 + 2. times… (More)

- Rolf Klein, Kurt Mehlhorn, Stefan Meiser
- Comput. Geom.
- 1993

- Rolf Klein, Derick Wood
- STACS
- 1988

- Pankaj K. Agarwal, Rolf Klein, +4 authors Michael A. Soss
- Discrete & Computational Geometry
- 2008

The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe " ! $ # & % ') (time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain " ! $ # & % 1 0 2) (time algorithms… (More)