approximation algorithms

Approximation ratio for k-outerplanar graphs ★★

Author(s): Bentz

\begin{conjecture} Is the approximation ratio for the \emph{Maximum Edge Disjoint Paths} (MaxEDP) or the \emph{Maximum Integer Multiflow} problem (MaxIMF) bounded by a constant in $k$-outerplanar graphs or tree-width graphs? \end{conjecture}

Keywords: approximation algorithms; planar graph; polynomial algorithm

Approximation Ratio for Maximum Edge Disjoint Paths problem ★★

Author(s): Bentz

\begin{conjecture} Can the approximation ratio $O(\sqrt{n})$ be improved for the Maximum Edge Disjoint Paths problem (MaxEDP) in planar graphs or can an inapproximability result stronger than $\mathcal{APX}$-hardness? \end{conjecture}

Keywords: approximation algorithms; Disjoint paths; planar graph; polynomial algorithm

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