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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2002: Graph-Theoretic Concepts in Computer Science pp 211–222Cite as

The Complexity of Approximating the Oriented Diameter of Chordal Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

Abstract

The oriented diameter of a (undirected) graph G is the smallest diameter among all the diameters of strongly connected orientations of G. We study algorithmic aspects of determining the oriented diameter of a chordal graph. We — give a linear time algorithm such that, for a given chordal graph G, either concludes that there is no strongly connected orientation of G, or finds a strongly connected orientation of G with diameter at most twice the diameter of G plus one; — prove that the corresponding decision problem remains NP-complete even when restricted to a small subclass of chordal graphs called split graphs; — show that unless P = NP, there is neither a polynomial-time absolute approximation algorithm nor an α-approximation (for every α< 3/2 ) algorithm computing oriented diameter of a chordal graph.

The work of IR and MM is partially supported by FONDAP on Applied Mathematics, Fondecyt 1020611 and Fondecyt 1010442. Part of this job was done while FVF was a postdoc at CMM, supported by FONDAP. FVF acknowledges support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies).

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Author information

Authors and Affiliations

  1. Heinz Nixdorf Institute and Paderborn University, Fürstenallee 11, D-33102, Paderborn, Germany

    Fedor V. Fomin

  2. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático UMR 2071-CNRS, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile

    Martín Matamala & Ivan Rapaport

Authors
  1. Fedor V. Fomin
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  2. Martín Matamala
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  3. Ivan Rapaport
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

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© 2002 Springer-Verlag Berlin Heidelberg

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Fomin, F.V., Matamala, M., Rapaport, I. (2002). The Complexity of Approximating the Oriented Diameter of Chordal Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_19

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  • DOI: https://doi.org/10.1007/3-540-36379-3_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

  • eBook Packages: Springer Book Archive

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