A Reliable Area Reduction Technique for Solving Circle Packing Problems

Abstract We are dealing with the optimal, i.e. densest packings of congruent circles into the unit square. In the recent years we have built a numerically reliable, verified method using interval arithmetic computations, which can be regarded as a `computer-assisted proof'. An efficient algorithm has been published earlier for eliminating large sets of suboptimal points of the equivalent point packing problem. The present paper discusses an interval arithmetic based version of this tool, implemented as an accelerating device of an interval branch

• Type: Journal
• Year: 2006
• Where: COMPUTING
• Authors: Mihály Csaba Markót, Tibor Csendes
• Keywords: COMPUTING 2006, Interval Arithmetic, Interval Arithmetic Computations, Interval Branch­and­bound Optimization