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PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
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DTSTAMP:20260525T035932Z
UID:Seminar-ACTO-493@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Nikhil Mande:MAILTO:Nikhil.Mande@liverpool
DTSTART:20190306T140000
DTEND:20190306T150000
SUMMARY:Algorithms, Complexity Theory and Optimisation Series
DESCRIPTION:Dr Paul Bell: Towards Uniform Online Spherical Tessellations\n\nWe study the problem of uniformly placing a set of N points onto the 2-sphere in the online setting, measured by studying the gap ratio from discrepancy theory. We start with some applications of this problem in various domains. We then propose a two-phase online algorithm, which uses a regular icosahedron in phase 1,\nand a recursive triangular dissection of each independent face of the icosahedron in phase 2 to improve the previous upper-bound for the gap ratio from 3.69 to 2.84. We also prove the first lower bound for the problem of 1.618 (the golden ratio). Our proof ideas use techniques from spherical trigonometry, geometry and spherical calculus.\nWe conclude with some open problems.\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=493
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