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Complexity of approximating the oriented diameter of chordal graphs

✍ Scribed by Fedor V. Fomin; Martín Matamala; Ivan Rapaport

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
135 KB
Volume
45
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The oriented diameter of a bridgeless connected undirected (bcu) 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 (a) construct a linear‐time approximation algorithm that, for a given chordal bcu graph G, finds a strongly connected orientation of G with diameter at most one plus twice the oriented diameter of G; (b) prove that, for every k ≥ 2 and k # 3, to decide whether a chordal (split for k = 2) bcu graph G admits an orientation of diameter k is NP‐complete; (c) show that, unless P = NP, there is neither a polynomial‐time absolute approximation algorithm nor an α‐approximation algorithm that computes the oriented diameter of a bcu chordal graph for α < ${3\over2}$. © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 255–269, 2004

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