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Stochastic Covering and Adaptivity

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LATIN 2006: Theoretical Informatics (LATIN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3887))

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Abstract

We introduce a class of “stochastic covering” problems where the target set X to be covered is fixed, while the “items” used in the covering are characterized by probability distributions over subsets of X. This is a natural counterpart to the stochastic packing problems introduced in [5]. In analogy to [5], we study both adaptive and non-adaptive strategies to find a feasible solution, and in particular the adaptivity gap, introduced in [4].

It turns out that in contrast to deterministic covering problems, it makes a substantial difference whether items can be used repeatedly or not. In the model of Stochastic Covering with item multiplicity, we show that the worst case adaptivity gap is Θ(log d), where d is the size of the target set to be covered, and this is also the best approximation factor we can achieve algorithmically. In the model without item multiplicity, we show that the adaptivity gap for Stochastic Set Cover can be Ω(d). On the other hand, we show that the adaptivity gap is bounded by O(d 2), by exhibiting an O(d 2)-approximation non-adaptive algorithm.

Research Supported in part by NSF grants CCR-0098018 and ITR-0121495, and ONR grant N00014-05-1-0148.

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Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Michel Goemans

  2. Microsoft Research, Redmond, WA, 98052, USA

    Jan Vondrák

Authors
  1. Michel Goemans
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  2. Jan Vondrák
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Editor information

Editors and Affiliations

  1. School of Business, Universidad Adolfo Ibáñez, Chile

    José R. Correa

  2. Dept. of Computer Science, University of Chile, Blanco Encalada 2120, 3er piso, Santiago, Chile

    Alejandro Hevia

  3. Dept. Ing. Matemática & Ctr. de Modelamiento Matemático, UMI 2807 U. Chile–CNRS, Chile

    Marcos Kiwi

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© 2006 Springer-Verlag Berlin Heidelberg

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Goemans, M., Vondrák, J. (2006). Stochastic Covering and Adaptivity. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_50

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  • DOI: https://doi.org/10.1007/11682462_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32755-4

  • Online ISBN: 978-3-540-32756-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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