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We propose to look at the computational complexity of 2-dimensional geometric optimization problems on a finite point set with respect to the number of inner points (that is, points in the interior of the convex hull). As a case study, we consider the minimum weight triangulation problem. Finding a minimum weight triangulation for a set of n points in the… (More)

- Oswin Aichholzer, Thomas Hackl, +4 authors Birgit Vogtenhuber
- Graphs and Combinatorics
- 2009

Let S be a set of n points in general position in the plane. Together with S we are given a set of parity constraints, that is, every point of S is labeled either even or odd. A graph G on S satisfies the parity constraint of a point p ∈ S, if the parity of the degree of p in G matches its label. In this paper we study how well various classes of planar… (More)

- Michael Hoffmann, Csaba D. Tóth
- Graphs and Combinatorics
- 2014

It is shown that every disconnected vertex-colored plane straight line graph with no isolated vertices can be augmented (by adding edges) into a connected plane straight line graph such that the new edges respect the coloring and the degree of every vertex increases by at most two. The upper bound for the increase of vertex degrees is best possible: there… (More)

- Susan Hert, Michael Hoffmann, Lutz Kettner, Sylvain Pion, Michael Seel
- Comput. Geom.
- 2001

Geometric algorithms are based on geometric objects such as points, lines and circles. The term kernel refers to a collection of representations for constant-size geometric objects and operations on these representations. This paper describes how such a geometry kernel can be designed and implemented in C++, having special emphasis on adaptability,… (More)

- Robert Haas, Michael Hoffmann
- Theor. Comput. Sci.
- 2004

Consider the following problem, that we call “Chordless Path through Three Vertices” or CP3V, for short: Given a simple undirected graph G = (V,E), a positive integer k, and three distinct vertices s, t, and v ∈ V , is there a chordless path from s via v to t in G that consists of at most k vertices? In a chordless path, no two vertices are connected by an… (More)

- Vladimir G. Deineko, Michael Hoffmann, Yoshio Okamoto, Gerhard J. Woeginger
- Oper. Res. Lett.
- 2004

We study the traveling salesman problem (TSP) in the 2-dimensional Euclidean plane. The problem is NP-hard in general, but trivial if the points are in convex position. In this paper, we investigate the influence of the number of inner points (i.e., points in the interior of the convex hull) on the computational complexity of the problem. We give two simple… (More)

- Heiner Lasi, Peter Fettke, Hans-Georg Kemper, Thomas Feld, Michael Hoffmann
- Business & Information Systems Engineering
- 2014

Industry is the part of an economy that produces material goods which are highly mechanized and automatized. Ever since the beginning of industrialization, technological leaps have led to paradigm shifts which today are ex-post named “industrial revolutions”: in the field of mechanization (the so-called 1st industrial revolution), of the intensive use of… (More)

- Erik D. Demaine, Martin L. Demaine, Michael Hoffmann, Joseph O'Rourke
- Comput. Geom.
- 2003

We prove NP-hardness of a wide class of pushing-block puzzles similar to the classic Sokoban, generalizing several previous results [5, 6, 9, 10, 15, 17]. The puzzles consist of unit square blocks on an integer lattice; all blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants… (More)

- Michael Hoffmann, Marius Wanko, +6 authors Marcus Elstner
- Journal of the American Chemical Society
- 2006

The mechanism of color tuning in the rhodopsin family of proteins has been studied by comparing the optical properties of the light-driven proton pump bacteriorhodopsin (bR) and the light detector sensory rhodopsin II (sRII). Despite a high structural similarity, the maximal absorption is blue-shifted from 568 nm in bR to 497 nm in sRII. The molecular… (More)

- Michael Hoffmann, Csaba D. Tóth
- CCCG
- 2001

We show that the segment endpoint visibility graph of any finite set of disjoint line segments in the plane admits a simple Hamiltonian polygon, if not all segments are collinear. This proves a conjecture of Mirzaian.