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arXiv · 2302.05526

A Linear Delay Algorithm for Enumeration of 2-Edge/Vertex-connected Induced Subgraphs

Takumi Tada·Kazuya Haraguchi
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Abstract

For a set system $(V,{\mathcal C}\subseteq 2^V)$, we call a subset $C\in{\mathcal C}$ a component. A nonempty subset $Y\subseteq C$ is a minimal removable set (MRS) of $C$ if $C\setminus Y\in{\mathcal C}$ and no proper nonempty subset $Z\subsetneq Y$ satisfies $C\setminus Z\in{\mathcal C}$. In this paper, we consider the problem of enumerating all components in a set system such that, for every two components $C,C'\in{\mathcal C}$ with $C'\subsetneq C$, every MRS $X$ of $C$ satisfies either $X\subseteq C'$ or $X\cap C'=\emptyset$. We provide a partition-based algorithm for this problem, which yields the first linear delay algorithms to enumerate all 2-edge-connected induced subgraphs, and to enumerate all 2-vertex-connected induced subgraphs.

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Takumi Tada, Kazuya Haraguchi. 2023-02-10. A Linear Delay Algorithm for Enumeration of 2-Edge/Vertex-connected Induced Subgraphs. https://arxiv.org/abs/2302.05526

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