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arXiv · 2311.15639

On Approximating Cutwidth and Pathwidth

Nikhil Bansal·Dor Katzelnick·Roy Schwartz
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Abstract

We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $ \log^{1+o(1)}(n)$ approximation for the problem, substantially improving upon the previous poly-logarithmic guarantees based on the standard recursive balanced partitioning approach of Leighton and Rao (FOCS'88). Our key idea is a new metric decomposition procedure that is suitable for handling min-max objectives, which could be of independent interest. We also use this to show other results, including an improved $ \log^{1+o(1)}(n)$ approximation for computing the pathwidth of a graph.

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Nikhil Bansal, Dor Katzelnick, Roy Schwartz. 2023-11-27. On Approximating Cutwidth and Pathwidth. https://arxiv.org/abs/2311.15639

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