2,153 research outputs found
A tight analysis of Kierstead-Trotter algorithm for online unit interval coloring
Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their
algorithm is an optimal online algorithm for the online interval coloring
problem. In this paper, for online unit interval coloring, we show that the
number of colors used by the Kierstead-Trotter algorithm is at most , where is the size of the maximum clique in a given
graph , and it is the best possible.Comment: 4 page
Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam
We propose a stereographical-visualization scheme for a polarization state by
two-dimensional imaging of a weak value with a single setup. The key idea is to
employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in
weak measurement. Our scheme has the advantage that we can extract information
on the polarization state from the single image in which the zero-intensity
point of the optical vortex beam corresponds to a stereographic projection
point of the Poincare sphere. We experimentally perform single-setup weak
measurement to validate the stereographical relationship between the
polarization state on the Poincare sphere and the location of the
zero-intensity point.Comment: 6 pages, 4 figure
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