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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

- Anke Behnke, Matthias Engel, Richard Christen, Markus Nebel, Rolf R Klein, Thorsten Stoeck
- Environmental microbiology
- 2011

Initial environmental pyrosequencing studies suggested highly complex protistan communities with phylotype richness decisively higher than previously estimated. However, recent studies on individual bacteria or artificial bacterial communities evidenced that pyrosequencing errors may skew our view of the true complexity of microbial communities. We… (More)

- 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)

- 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)

- 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)

- 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.

1 Partially supported by the Deutsche Forschungsgemeinschaft, grant Kl 655 2-2.

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

Abstract Voronoi diagrams were introduced by R . Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis ofVoronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(nlogn) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new algorithm has the following advantages… (More)