Circle Packing: Experiments In Discrete Analytic Function Theory

Circle Packing: Experiments In Discrete Analytic Function Theory

Discrete Analytic Function

Formulation symmetries in circle packing

The performance of Branch-and-Bound algorithms is severely impaired by the presence of symmetric optima in a given problem. We describe a method for the automatic detection of formulation symmetries in MINLP instances. A software implementation of this method is used to conjecture the group structure of the problem symmetries of packing equal circles in a square. We provide a proof of the conje...

Recursive circle packing problems

This paper presents a class of packing problems where circles may be placed either inside or outside other circles, the whole set being packed in a rectangle. This corresponds to a practical problem of packing tubes in a container; before being inserted in the container, tubes may be put inside other tubes in a recursive fashion. A variant of the greedy randomized adaptive search procedure is p...

Circle Packing Explorations

Circle packing can be seen as the art of placing tangent circles on the plane, leaving as little unoccupied space as possible. Circle packing is a very attractive field of mathematics, from several points of view. It contains interesting and complex questions, both mathematical and algorithmical, and keeps its properties through a wide range of geometric transformations. There are several ways ...