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Approximation Hierarchies for the cone of flow matrices (2018)

Sagnol, Guillaume ; Blanco, Marco ; Sauvage, Thibaut

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Publication Date: 2020-08-05

Description: 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.

Language: English

Type: conferenceobject , doc-type:conferenceObject

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