Matrix Scaling: a New Heuristic for the Feedback Vertex Set Problem

James M. Shook; Isabel Beichl

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arXiv · 2503.10780

Matrix Scaling: a New Heuristic for the Feedback Vertex Set Problem

James M. Shook·Isabel Beichl

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Abstract

For a digraph $G$, a set $F\subseteq V(G)$ is said to be a feedback vertex set (FVS) if $G-F$ is acyclic. The problem of finding a smallest FVS is NP-hard. We present a matrix scaling technique for finding feedback vertex sets in un-weighted directed graphs that runs in $O(|F|\log(|V|)|V|^{2})$ time. Our technique is empirically shown to produce smaller feedback vertex sets than other known heuristics and in a shorter amount of time.

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BibTeX RIS

James M. Shook, Isabel Beichl. 2025-03-13. Matrix Scaling: a New Heuristic for the Feedback Vertex Set Problem. https://arxiv.org/abs/2503.10780

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