Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Fillings - A new spatial subdivision problem related to packing
  and covering   We present filling as a new type of spatial subdivision problem that is
related to covering and packing. Filling addresses the optimal placement of
overlapping objects lying entirely inside an arbitrary shape so as to cover the
most interior volume. In n-dimensional space, if the objects are polydisperse
n-balls, we show that solutions correspond to sets of maximal n-balls and the
solution space can reduced to the medial axis of a shape. We examine the
structure of the solution space in two dimensions. For the filling of polygons,
we provide detailed descriptions of a heuristic and a genetic algorithm for
finding solutions of maximal discs. We also consider the properties of ideal
distributions of N discs in polygons as N approaches infinity.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th