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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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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