Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Graph Theoretical Approach to Network Encoding Complexity   Consider an acyclic directed network $G$ with sources $S_1, S_2,..., S_l$ and
distinct sinks $R_1, R_2,..., R_l$. For $i=1, 2,..., l$, let $c_i$ denote the
min-cut between $S_i$ and $R_i$. Then, by Menger's theorem, there exists a
group of $c_i$ edge-disjoint paths from $S_i$ to $R_i$, which will be referred
to as a group of Menger's paths from $S_i$ to $R_i$ in this paper. Although
within the same group they are edge-disjoint, the Menger's paths from different
groups may have to merge with each other. It is known that by choosing Menger's
paths appropriately, the number of mergings among different groups of Menger's
paths is always bounded by a constant, which is independent of the size and the
topology of $G$. The tightest such constant for the all the above-mentioned
networks is denoted by $\mathcal{M}(c_1, c_2,..., c_2)$ when all $S_i$'s are
distinct, and by $\mathcal{M}^*(c_1, c_2,..., c_2)$ when all $S_i$'s are in
fact identical. It turns out that $\mathcal{M}$ and $\mathcal{M}^*$ are closely
related to the network encoding complexity for a variety of networks, such as
multicast networks, two-way networks and networks with multiple sessions of
unicast. Using this connection, we compute in this paper some exact values and
bounds in network encoding complexity using a graph theoretical approach.

8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc