TY - CONF A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - Approximation Hierarchies for the cone of flow matrices T2 - INOC 2017 – 8th International Network Optimization Conference N2 - Let $G$ be a directed acyclic graph with $n$ arcs, a source $s$ and a sink $t$. We introduce the cone $K$ of flow matrices, which is a polyhedral cone generated by the matrices $1_P 1_P^T \in R^{n\times n}$, where $1_P\in R^n$ is the incidence vector of the $(s,t)$-path $P$. Several combinatorial problems reduce to a linear optimization problem over $K$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of $K$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities. Y1 - 2018 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6844 VL - 64 SP - 275 EP - 284 ER -