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arXiv · 2605.17396

Fast and Practical Single-Exponential Algorithms for Branchwidth

Taiki Kaneda·Yasuaki Kobayashi·Hisao Tamaki
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Abstract

In this paper, we present exact exponential algorithms for computing branchwidth that are fast both in theory and in practice. The running times of these algorithms are single-exponential in the number of vertices. Our basic algorithm is based on a conceptually simple recurrence on vertex sets and computes the branchwidth of an $n$-vertex hypergraph in time $\mathcal{O}^*(4^n)$. This is the first single-exponential time algorithm for hypergraphs. We have two algorithms tailored specifically for graphs. The first algorithm runs in time $\mathcal{O}(3.293^n)$, improving upon the previously best-known running time of $\mathcal{O}(3.4652^n)$ [Fomin-Mazoit-Todinca, DAM 2009]. Moreover, our computational experiment shows that it overwhelmingly outperforms state-of-the-art practical algorithms for computing branchwidth. The second algorithm is a candidate for a theoretical improvement: we conjecture that it runs in time $\mathcal{O}(c^n)$ for some constant $c$ that is smaller than 3.293. In practice, it performs significantly better on some instances that are hard for the first algorithm.

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Taiki Kaneda, Yasuaki Kobayashi, Hisao Tamaki. 2026-05-17. Fast and Practical Single-Exponential Algorithms for Branchwidth. https://arxiv.org/abs/2605.17396

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