Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A partial differential equations approach to defeating partisan
  gerrymandering   We introduce a novel partial differential equations approach for addressing
the problem of partisan gerrymandering. Our method is based on volume
preserving curvature flow, a partial differential equation which we adapt to
smooth voting district boundaries while preserving equal voting populations. We
show that every step of the flow minimizes a "compactness energy", allowing us
to demonstrate that our method produces more "compact" and reasonable district
maps. We compute the flow using a variant of "auction dynamics" --- an
efficient MBO type algorithm for computing volume preserving curvature flows.
This "auction dynamics" approach can be used to generate hundreds of reasonable
maps in a matter of seconds without parallelization. The compactness energy
provides a way of comparing proposed districtings of a given state. We
demonstrate both the map generation and map comparison features of our approach
for several different states.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph