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Asymptotic Bounds on Minimun Number of Disks Required to Hide a Disk

Authors:
Natasa Jovanovic
Jan Korst
Zharko Aleksovski
Radivoje Jovanovic

Keywords: asymptotic bounds; blocking set; hiding disk.

Abstract:
We consider the problem of blocking all rays emanating from a closed unit disk with a minimum number of closed unit disks in the two-dimensional space, where the minimum distance from a disk to any other disk is given. We study the asymptotic behavior of the minimum number of disks as the minimum mutual distance approaches infinity. Using a regular ordering of disks on concentric circular rings we derive an upper bound and prove that the minimum number of disks required for blocking is quadratic in the minimum distance between the disks.

Pages: 160 to 165

Copyright: Copyright (c) IARIA, 2010

Publication date: October 25, 2010

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-61208-101-4

Location: Florence, Italy

Dates: from October 25, 2010 to October 30, 2010