We consider the parameterized problem, whether a given set of n disks (of bounded radius) in the Euclidean plane contains k non-intersecting disks. We expose an algorithm running in time n √ , that is—to our knowledge—the first algorithm for this problem with running time bounded by an exponential with a sublinear exponent. The results are based on a new “geometric √ ·-separator theorem” which ...

In this paper I examine the connection between symmetry and modality from the perspective of ‘reduction’ methods in geometric mechanics. I begin by setting the problem up as a choice between two opposing views: reduction and non-reduction. I then discern four views on the matter in the literature; they are distinguished by their advocation of distinct geometric spaces as representing ‘reality’....