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A Polynomial Delay Algorithm for Enumerating 2-Edge-Connected Induced Subgraphs

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Frontiers in Algorithmics (FAW 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12340))

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Abstract

The problem of enumerating connected induced subgraphs of a given graph is classical and studied well. It is known that connected induced subgraphs can be enumerated in constant time for each subgraph. In this paper, we focus on highly connected induced subgraphs. The most major concept of connectivity on graphs is vertex connectivity. For vertex connectivity, some enumeration problem settings are proposed and enumeration algorithms are proposed, such as k-vertex connected spanning subgraphs. In this paper, we focus on another major concept of graph connectivity, edge-connectivity. This is motivated by the problem of finding evacuation routes in road networks. In evacuation routes, edge-connectivity is important, since highly edge-connected subgraphs ensure multiple routes between two vertices. In this paper, we consider the problem of enumerating 2-edge-connected induced subgraphs of a given graph. We present an algorithm that enumerates 2-edge-connected induced subgraphs of an input graph G with n vertices and m edges. Our algorithm enumerates all the 2-edge-connected induced subgraphs in \(\text {O}(n^3 m \left| \mathcal {S}_G\right| )\) time, where \(\mathcal {S}_G\) is the set of the 2-edge-connected induced subgraphs of G. Moreover, by slightly modifying the algorithm, we have a polynomial delay enumeration algorithm for 2-edge-connected induced subgraphs.

This work was supported by JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11812.

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Notes

  1. 1.

    A closed-ear decomposition is an ear decomposition if every ear in the decomposition is an open ear.

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Authors and Affiliations

  1. Faculty of Science and Engineering, Iwate University, Ueda 4-3-5, Morioka, Iwate, Japan

    Yusuke Sano, Katsuhisa Yamanaka & Takashi Hirayama

Authors
  1. Yusuke Sano
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  2. Katsuhisa Yamanaka
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  3. Takashi Hirayama
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Correspondence to Katsuhisa Yamanaka .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong, China

    Minming Li

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Sano, Y., Yamanaka, K., Hirayama, T. (2020). A Polynomial Delay Algorithm for Enumerating 2-Edge-Connected Induced Subgraphs. In: Li, M. (eds) Frontiers in Algorithmics. FAW 2020. Lecture Notes in Computer Science(), vol 12340. Springer, Cham. https://doi.org/10.1007/978-3-030-59901-0_2

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  • DOI: https://doi.org/10.1007/978-3-030-59901-0_2

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