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An Efficient Algorithm for Enumerating Induced Subgraphs with Bounded Degeneracy

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Combinatorial Optimization and Applications (COCOA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11346))

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Abstract

We propose a polynomial delay and polynomial space algorithm for the enumeration of k-degenerate induced subgraphs in a given graph. A graph G is k-degenerate if each of its induced subgraphs has a vertex of degree at most k. The degeneracy is considered as an indicator of the sparseness of the graph. Real-world graphs such as road networks, social networks and internet networks often have small degeneracy. Compared to other kinds of graph classes, bounded degeneracy does not give many structural properties such as induced subgraph free, or minor free. From this, using bounded degeneracy to reduce the time complexity is often not trivial. In this paper, we investigate ways of handling the degeneracy and propose an efficient algorithm for the k-degenerate induced subgraph enumeration. The time complexity is \(\mathcal {O}\left( \min \left\{ \varDelta + kk', (k')^2\right\} \right) \) time per solution with polynomial preprocessing time and the space complexity is linear in the input graph size, where \(\varDelta \) and \(k'\) are the maximum degree and the degeneracy of the input graph.

This work was supported by JST CREST, Grant Number JPMJCR1401, Japan.

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Kunihiro Wasa & Takeaki Uno

Authors
  1. Kunihiro Wasa
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  2. Takeaki Uno
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Correspondence to Kunihiro Wasa .

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Editors and Affiliations

  1. Department of Computer Science, Kennesaw State University, Marietta, GA, USA

    Donghyun Kim

  2. Department of Mathematics and Computer Science, North Carolina Central University, Durham, NC, USA

    R. N. Uma

  3. Department of Computer Science, Georgia State University, Atlanta, GA, USA

    Alexander Zelikovsky

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Wasa, K., Uno, T. (2018). An Efficient Algorithm for Enumerating Induced Subgraphs with Bounded Degeneracy. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_3

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  • DOI: https://doi.org/10.1007/978-3-030-04651-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04650-7

  • Online ISBN: 978-3-030-04651-4

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