Showing papers on "Angular resolution (graph drawing) published in 2015"
24 Sep 2015
TL;DR: Two new algorithms are introduced that perform better in terms of edge length and minimal face aspect ratio than the current algorithms, which are based on a sequence of dual edge contractions and a recursion of nested cycles.
Abstract: A drawing of a graph can be understood as an arrangement of geometric objects. In the most natural setting the arrangement is formed by straight-line segments. Every cubic planar 3-connected graph with n vertices has such a drawing with only $$n/2 + 3$$ segments, matching the lower bound. This result is due to Mondal et al. [J. of Comb. Opt., 25], who gave an algorithm for constructing such drawings.
We introduce two new algorithms that also produce drawings with $$n/2 + 3$$ segments. One algorithm is based on a sequence of dual edge contractions, the other is based on a recursion of nested cycles. We also show a flaw in the algorithm of Mondal et al. and present a fix for it. We then compare the performance of these three algorithms by measuring angular resolution, edge length and face aspect ratio of the constructed drawings. We observe that the corrected algorithm of Mondal et al. mostly outperforms the other algorithms, especially in terms of angular resolution. However, the new algorithms perform better in terms of edge length and minimal face aspect ratio.
11 citations
2 Dec 2015
Abstract: AGILE (LightImagerforGamma-rayAstrophysics) is a small scientific satellite for the detection of cosmicg-ray sources in the energy range 30 MeV-50 GeV with a very field of view (1/4 of the sky). It is planned to be operational in the years 2003-2006, a period in which no other γ-ray mission in the same energy range is foreseen. The AGILE scientific instrument is made of a silicon-tungsten Tracker, aCsI(Tl) Minicalorimeter, an Anticoincidence system and a X-ray imaging detector sensitive in the 10-40keV range. We present here a detailed description of the architectural design of the Silicon. Tracker with it strigger and readout logic, and the performance of the detector prototype during a test beam period at the CERN PS in May 2000. The Tracker performance is described in terms of position resolution and signal to noise ratio for on-axis and off-axis incident charged particles. The measured 40 μm resolution for a large range of incident angles will provide an excellent angular resolution for cosmic γ-ray imaging.