Abstract
We consider dual classes of geometric coverage problems, in which disks, corresponding to coverage regions of sensors, are used to cover a region or set of points in the plane. The first class of problems involve assigning radii to already-positioned sensors (being cheap ). The second class of problems are motivated by the fact that the sensors may, because of practical difficulties, be positioned with only approximate accuracy (being flexible ). This changes the character of some coverage problems that solve for optimal disk positions or disk sizes, ordinarily assuming the disks can be placed precisely in their chosen positions, and motivates new problems. Given a set of disk sensor locations, we show for most settings how to assign either (near-)optimal radius values or allowable amounts of placement error. Our primary results are 1) in the 1-d setting we give a faster dynamic programming algorithm for the (linear) sensor radius problem; and 2) we find a max-min fair set of radii for the 2-d continuous problems in polynomial time. We also give results for other settings, including fast approximation algorithms for the 1-d continuous case.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.