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Augmenting Graphs to Minimize the Diameter

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Abstract

We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT \(4\)-approximation algorithm for the problem.

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Notes

  1. After the publication of the conference version of this paper [9] and after the first submission of the present journal paper, James Nastos informed us about a paper whose results overlap with the intractability results of this paper. Namely, Gao, Hare, and Nastos [12] proved that the bcmd problem with unit weights and costs is \({ W[2]}\)-hard, for every target diameter \(d\ge 2\). Their reduction is from “dominating set” and is similar to the one we present in this paper. We apologize to the authors of [12] for not being aware of their previous result.

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Acknowledgments

A preliminary version of this paper was presented in [9]. FF acknowledges support from the Australian Research Council (grant DE140100708). SG acknowledges support from the Australian Research Council (grant DE120101761). JG acknowledges support from the Australian Research Council (grant FT100100755). NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.

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Authors and Affiliations

  1. University of Sydney, Sydney, Australia

    Fabrizio Frati & Joachim Gudmundsson

  2. University of New South Wales, Sydney, Australia

    Serge Gaspers

  3. NICTA, Sydney, Australia

    Serge Gaspers & Joachim Gudmundsson

  4. Macquarie University, Sydney, Australia

    Luke Mathieson

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  1. Fabrizio Frati
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  2. Serge Gaspers
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  3. Joachim Gudmundsson
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  4. Luke Mathieson
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Correspondence to Joachim Gudmundsson.

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Frati, F., Gaspers, S., Gudmundsson, J. et al. Augmenting Graphs to Minimize the Diameter. Algorithmica 72, 995–1010 (2015). https://doi.org/10.1007/s00453-014-9886-4

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