A bounded space algorithm for online circle packing

• We present results for the Online Circle Packing Problem.
• A 2.4394-competitive bounded space algorithm.
• A 2.292 lower bound on the competitive ratio of any online bounded space algorithm.
• We combine Integer Linear Programming with Constraint Programming for computations.

We study the Online Circle Packing Problem where we need to pack circles that arrive online in square bins with the objective to minimize the number of bins used. An online algorithm is said to have bounded space if at any given time, only a constant number of bins are open, circles are packed only in open bins and once a bin is closed it cannot be reopened. In particular, we present a 2.4394-competitive bounded space algorithm for this problem and a 2.2920 lower bound on the competitive ratio of any online bounded space algorithm for this problem.