Abstract
In this paper, we study the online class cover problem where a (finite or infinite) family F of geometric objects and a set Pr of red points in Rd are given a prior, and blue points from Rd arrives one after another. Upon the arrival of a blue point, the online algorithm must make an irreversible decision to cover it with objects from F that do not cover any points of Pr. The objective of the problem is to place a minimum number of objects. When F consists of axis-parallel unit squares in R2, we prove that the competitive ratio of any deterministic online algorithm is Ω(log|Pr|), and also propose an O(log|Pr|)-competitive deterministic algorithm for the problem.
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.