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Directed vertex-connectivity augmentation

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Abstract

The problem of finding a smallest set of new edges to be added to a given directed graph to make it k-vertex-connected was shown to be polynomially solvable recently in [6] for any target connectivity k ≤ 1. However, the algorithm given there relied on the ellipsoid method. Here we refine some results of [6] which makes it possible to construct a combinatorial algorithm which is polynomial for any fixed k. Short proofs for (extensions of) some earlier results related to this problem will also be given.

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Authors and Affiliations

  1. Department of Operations Research, Eötvös University, H-1088 Budapest, Rákóczi út 5, Hungary, and Ericsson Traffic Laboratory, Laborc u. 1, Budapest, Hungary, e-mail: frank@cs.elte.hu., HU

    András Frank

  2. CWI, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands, e-mail: jordan@cs.elte.hu. Current address: BRICS, Department of Computer Science, University of Aarhus, DK-8000 Aarhus C, Denmark, NL

    Tibor Jordán

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  1. András Frank
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  2. Tibor Jordán
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Received August 1995 / Revised version received January 1997 Published online March 16, 1999

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Frank, A., Jordán, T. Directed vertex-connectivity augmentation. Math. Program. 84, 537–553 (1999). https://doi.org/10.1007/s101070050038

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  • DOI: https://doi.org/10.1007/s101070050038

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