Abstract
The problem of finding the largest empty axis-parallel box amidst a point configuration is a classical problem in computational geometry. It is known that the volume of the largest empty box is of asymptotic order 1∕n for n→∞ and fixed dimension d. However, it is natural to assume that the volume of the largest empty box increases as d gets larger. In the present paper we prove that this actually is the case: for every set of n points in [0,1]d there exists an empty box of volume at least cdn−1, where cd→∞ as d→∞. More precisely, cd is at least of order roughly logd.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
