Abstract

This paper addresses the computational complexity of optimization problems dealing with the covering of points in the discrete plane by rectangles. Particularly we prove the NP-hardness of such a problem(class) defined by the following objective function: Simultaneously minimize the total area, the total circumference and the number of rectangles used for covering (where the length of every rectangle side is required to lie in a given interval). By using a tiling argument we also prove that a variant of this problem, fixing only the minimal side length of rectangles, is NP-hard. Such problems may appear at the core of applications like data compression, image processing or numerically solving partial differential equations by multigrid computations.

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 call

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.