---

Cai et al.(2013) and  Cai and Han (2014) presented the polynomial time algorithms for two-pair and three-pair networks with common bottleneck links, respectively. Also, Chen and HaiBin(2012) proposed a non-polynomial time algorithms for $n$-pair networks with common bottleneck links, where $n$ is an arbitrary integer. This paper presents a new sufficient and necessary condition to determine the solvability of single rate $n$-pair networks with common bottleneck links, which concludes a polynomial time algorithm for $n$-pair networks with common bottleneck links, where $n$ is an arbitrary integer. Our algorithm runs in $O(|V||E|^{2})$ time, where $|V|$ and $|E|$ are the number of nodes and links, respectively.

---

A sum-network is a directed acyclic network with multiple sources and multiple sinks where each sink  demands the sum of the independent information generated at the sources. The coding capacity of sum networks with independent sources has been investigated in Tripathy and Ramamoorthy(2015) and it was proven that the upper bound of the coding capacity of such networks is 1. In this paper,  it is shown that the upper bound of the coding capacity of a sum network with dependent sources is greater than 1 which is different from the obtained results in Tripathy and Ramamoorthy(2015).
 It is also shown that a non-solvable sum-network with independent sources can be converted to a solvable one when the sources have arbitrary dependencies