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Successive edge-connectivity augmentation problems

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,G1,G2,... of supergraphs of G such that Gi is a subgraph of Gj for any i<j and Gi is an optimal (l+i)-edge-connected augmentation of G for any i≥0.

In this paper we will show that the augmentation algorithm of A. Frank [3] can also be used to solve the corresponding Successive Edge-Augmentation Problem and implies (a stronger version of) the Successive Augmentation Property, even for some non-uniform demands.

In addition we show the – previously unknown – Successive Augmentation Property for directed edge-connectivity (in the case of uniform demands).

For several possible extensions and for the two vertex-connectivity versions counter-examples are given.

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Authors and Affiliations

  1. Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. Current address: Department of Mathematics and Statistics, Oakland University, Rochester, Michigan, 48309-4485, USA, CA

    Eddie Cheng

  2. CWI, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands. Current address: BRICS, Department of Computer Science, University of Aarhus, DK-8000 Aarhus C, Denmark, NL

    Tibor Jordán

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  1. Eddie Cheng
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  2. Tibor Jordán
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Received March 1995 / Revised version received February 1997 Published online March 16, 1999

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Cheng, E., Jordán, T. Successive edge-connectivity augmentation problems. Math. Program. 84, 577–593 (1999). https://doi.org/10.1007/s101070050041

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  • DOI: https://doi.org/10.1007/s101070050041

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