Rigorous packing of unit squares into a circle.

ABSTRACT: This paper considers the task of finding the smallest circle into which one can pack a fixed number of non-overlapping unit squares that are free to rotate. Due to the rotation angles, the packing of unit squares into a container is considerably harder to solve than their circle packing counterparts. Therefore, optimal arrangements were so far proved to be optimal only for one or two unit squares. By a computer-assisted method based on interval arithmetic techniques, we solve the case of three squares and find rigorous enclosures for every optimal arrangement of this problem. We model the relation between the squares and the circle as a constraint satisfaction problem (CSP) and found every box that may contain a solution inside a given upper bound of the radius. Due to symmetries in the se

SUBMITTER: Montanher T 

PROVIDER: S-EPMC6394747 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature