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arXiv · 2208.14841

On weighted graph separation problems and flow-augmentation

Eun Jung Kim·Tomáš Masařík·Marcin Pilipczuk·Roohani Sharma·Magnus Wahlström
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Abstract

One of the first application of the recently introduced technique of \emph{flow-augmentation} [Kim et al., STOC 2022] is a fixed-parameter algorithm for the weighted version of \textsc{Directed Feedback Vertex Set}, a landmark problem in parameterized complexity. In this note we explore applicability of flow-augmentation to other weighted graph separation problems parameterized by the size of the cutset. We show the following. -- In weighted undirected graphs \textsc{Multicut} is FPT, both in the edge- and vertex-deletion version. -- The weighted version of \textsc{Group Feedback Vertex Set} is FPT, even with an oracle access to group operations. -- The weighted version of \textsc{Directed Subset Feedback Vertex Set} is FPT. Our study reveals \textsc{Directed Symmetric Multicut} as the next important graph separation problem whose parameterized complexity remains unknown, even in the unweighted setting.

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Eun Jung Kim, Tomáš Masařík, Marcin Pilipczuk, Roohani Sharma, Magnus Wahlström. 2022-08-31. On weighted graph separation problems and flow-augmentation. https://doi.org/10.1137/22m153118x

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