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Modifying networks to obtain low cost trees

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Graph-Theoretic Concepts in Computer Science (WG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1197))

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Abstract

We consider the problem of reducing the edge lengths of a given network so that the modified network has a spanning tree of small total length. It is assumed that each edge e of the given network has an associated function c e that specifies the cost of shortening the edge by a given amount and that there is a budget B on the total reduction cost. The goal is to develop a reduction strategy satisfying the budget constraint so that the total length of a minimum spanning tree in the modified network is the smallest possible over all reduction strategies that obey the budget constraint.

We show that in general the problem of computing an optimal reduction strategy for modifying the network as above is NP-hard and present the first polynomial time approximation algorithms for the problem, where the cost functions c e are allowed to be taken from a broad class of functions. We also present improved approximation algorithms for the class of treewidth-bounded graphs when the cost functions are linear. Our results can be extended to obtain approximation algorithms for more general network design problems such as those considered in [9, 10].

Research supported by Department of Energy under contract W-7405-ENG-36.

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Authors and Affiliations

  1. University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    S. O. Krumke, H. Noltemeier & K. U. Drangmeister

  2. Los Alamos Nat. Lab., P.O. Box 1663, MS M986, 87545, Los Alamos, NM, USA

    M. V. Marathe

  3. University at Albany - SUNY, 12222, Albany, NY, USA

    S. S. Ravi

Authors
  1. S. O. Krumke
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  2. H. Noltemeier
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  3. M. V. Marathe
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  4. S. S. Ravi
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  5. K. U. Drangmeister
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Editor information

Fabrizio d'Amore Paolo Giulio Franciosa Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Krumke, S.O., Noltemeier, H., Marathe, M.V., Ravi, S.S., Drangmeister, K.U. (1997). Modifying networks to obtain low cost trees. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_24

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  • DOI: https://doi.org/10.1007/3-540-62559-3_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62559-9

  • Online ISBN: 978-3-540-68072-7

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