Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar additive bases for rectangles   We study a generalization of additive bases into a planar setting. A planar
additive basis is a set of non-negative integer pairs whose vector sumset
covers a given rectangle. Such bases find applications in active sensor arrays
used in, for example, radar and medical imaging. The problem of minimizing the
basis cardinality has not been addressed before.
  We propose two algorithms for finding the minimal bases of small rectangles:
one in the setting where the basis elements can be anywhere in the rectangle,
and another in the restricted setting, where the elements are confined to the
lower left quadrant. We present numerical results from such searches, including
the minimal cardinalities for all rectangles up to $[0,11]\times[0,11]$, and up
to $[0,46]\times[0,46]$ in the restricted setting. We also prove asymptotic
upper and lower bounds on the minimal basis cardinality for large rectangles.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph