Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimization Approach to the Langberg-M\'edard Multiple Unicast
  Conjecture   The Langberg-M\'edard multiple unicast conjecture claims that for any
strongly reachable $k$-pair network, there exists a multi-flow with rate
$(1,1,\dots,1)$. In a previous work, through combining and concatenating the
so-called elementary flows, we have constructed a multi-flow with rate at least
$(\frac{8}{9}, \frac{8}{9}, \dots, \frac{8}{9})$ for any $k$. In this paper, we
examine an optimization problem arising from this construction framework. We
first show that our previous construction yields a sequence of asymptotically
optimal solutions to the aforementioned optimization problem. And furthermore,
based on this solution sequence, we propose a perturbation framework, which not
only promises a better solution for any $k \mod 4 \neq 2$ but also solves the
optimization problem for the cases $k=3, 4, \dots, 10$, accordingly yielding
multi-flows with the largest rate to date.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th