Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Maximum Rate of Networked Computation in a Capacitated Network   Given a capacitated communication network $\mathcal{N}$ and a function f that
needs to be computed on $\mathcal{N},$ we study the problem of generating a
computation and communication schedule in $\mathcal{N}$ to maximize the rate of
computation of f. Shah et. al.[IEEE Journal of Selected Areas in Communication,
2013] studied this problem when the computation schema $\mathcal{G}$ for f is a
tree. We define the notion of a schedule when $\mathcal{G}$ is a general DAG
and show that finding an optimal schedule is equivalent to finding the solution
of a packing LP. We prove that approximating the maximum rate is MAX SNP-hard
by looking at the packing LP. For this packing LP we prove that solving the
separation oracle of its dual is equivalent to solving the LP. The separation
oracle of the dual reduces to the problem of finding minimum cost embedding
given $\mathcal{N},\mathcal{G},$ which we prove to be MAX SNP-hard even when
$\mathcal{G}$ has bounded degree and bounded edge weights and $\mathcal{N}$ has
just three vertices. We present a polynomial time algorithm to compute the
maximum rate of function computation when $\mathcal{N}$ has two vertices by
reducing the problem to a version of submodular function minimization problem.
For the general $\mathcal{N}$ we study restricted class of schedules and its
equivalent packing LP. We observe that for this packing LP also the separation
oracle of its dual reduces to finding minimum cost embedding. A version of this
minimum cost embedding problem has been studied in literature. We present a
quadratic integer program for the minimum cost embedding problem and its linear
programming relaxation based on earthmover metric. We also present some
approximate algorithms for special classes of $\mathcal{G}.$

26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex