Learn More
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)
We generalize the notions of flippable and simultaneously flippable edges in a tri-angulation of a set S of points in the plane to so-called pseudo-simultaneously flippable edges. Such edges are related to the notion of convex decompositions spanned by S. We prove a worst-case tight lower bound for the number of pseudo-simultaneously flippable edges in a(More)
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)
The goal of this thesis is to give a better understanding of the linear complementarity problem with a P-matrix (PLCP). Finding a polynomial time algorithm for the PLCP is a longstanding open problem. Such an algorithm would settle the complexity status of many problems reducing to the PLCP. Most of the papers dealing with the PLCP look at it from an(More)
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)
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)
Hybrid Virtual Environment 3D (Hyve-3D) is a system to actively design inside Virtual Reality by a new model of interaction through a <i>3D cursor</i> that is specially envisioned to facilitate local and remote collaboration. It introduces a novel approach to the concept of the cursor inside the 3D virtual space, rethinking it as a drawing and control(More)
Bacteriorhodopsin is a proton-pumping membrane protein found in the plasma membrane of the archaeon Halobacterium salinarium. Light-induced isomerization of the retinal chromophore from all-trans to 13-cis leads to a sequence of five conformation-coupled proton transfer steps and the net transport of one proton from the cytoplasmic to the extracellular side(More)
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)