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Computing the Degeneracy of Large Graphs

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LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

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Abstract

Any ordering of the nodes of an n-node, m-edge simple undirected graph G defines an acyclic orientation of the edges in which each edge is oriented from the earlier node in the ordering to the later. The degeneracy on an ordering is the maximum outdegree it induces, and the degeneracy of a graph is smallest degeneracy of any node ordering. Small-degeneracy orderings have many applications.

We give an algorithm for generating an ordering whose degeneracy approximates the minimum possible, that is, it approximates the degeneracy of the graph. Although the optimal ordering itself can be computed in \(\mathcal{O}(m)\) time and \(\mathcal{O}(m)\) space, such algorithms are infeasible for large graphs. Our approximation algorithm is semi-streaming: it uses less space, can achieve a constant approximation ratio, and accesses the graph in logarithmic read-only passes.

Work supported by NSF Grants IIS-1247750 and CCF-1114930

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Authors and Affiliations

  1. Rutgers University, New Brunswick, NJ, 08901, USA

    Martín Farach-Colton & Meng-Tsung Tsai

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  1. Martín Farach-Colton
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  2. Meng-Tsung Tsai
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Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Farach-Colton, M., Tsai, MT. (2014). Computing the Degeneracy of Large Graphs. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_22

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

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