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International Colloquium on Automata, Languages, and Programming

ICALP 2010: Automata, Languages and Programming pp 490–502Cite as

Network Design via Core Detouring for Problems without a Core

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6198))

Abstract

Some of the currently best-known approximation algorithms for network design are based on random sampling. One of the key steps of such algorithms is connecting a set of source nodes to a random subset of them. In a recent work [Eisenbrand,Grandoni,Rothvoß,Schäfer-SODA’08], a new technique, core-detouring, is described to bound the mentioned connection cost. This is achieved by defining a sub-optimal connection scheme, where paths are detoured through a proper connected subgraph (core). The cost of the detoured paths is bounded against the cost of the core and of the distances from the sources to the core. The analysis then boils down to proving the existence of a convenient core.

For some problems, such as connected facility location and single-sink rent-or-buy, the choice of the core is obvious (i.e., the Steiner tree in the optimum solution). Other, more complex network design problems do not exhibit any such core. In this paper we show that core-detouring can be nonetheless successfully applied. The basic idea is constructing a convenient core by manipulating the optimal solution in a proper (not necessarily trivial) way. We illustrate that by presenting improved approximation algorithms for two well-studied problems: virtual private network design and single-sink buy-at-bulk.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma Tor Vergata, Via del Politecnico 1, 00133, Roma, Italy

    Fabrizio Grandoni

  2. Institute of Mathematics, EPFL, Lausanne, Switzerland

    Thomas Rothvoß

Authors
  1. Fabrizio Grandoni
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  2. Thomas Rothvoß
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

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Grandoni, F., Rothvoß, T. (2010). Network Design via Core Detouring for Problems without a Core. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_42

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  • DOI: https://doi.org/10.1007/978-3-642-14165-2_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14164-5

  • Online ISBN: 978-3-642-14165-2

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