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Hardness of Set Cover with Intersection 1

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Automata, Languages and Programming (ICALP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1853))

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Abstract

We consider a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(logn) factor in random polynomial time unless NP ⊆ ZTIME(n o(log logn)). We also observe that the main challenge in derandomizing this reduction lies in finding a hitting set for large volume combinatorial rectangles satisfying certain intersection properties. These properties are not satisfied by current methods of hitting set construction.

An example of a Set Covering problem with the intersection 1 property is the problem of covering a given set of points in two or higher dimensions using straight lines; any two straight lines intersect in at most one point. The best approximation algorithm currently known for this problem has an approximation factor of θ(logn), and beating this bound seems hard. We observe that this problem is Max-SNP-Hard.

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Author information

Authors and Affiliations

  1. MPI für Informatik, Saarbrücken

    V. S. Anil Kumar

  2. Department of Computer Science, Hong Kong University of Science andTechnology, Hong Kong

    Sunil Arya

  3. Department of Computer Science and Automation, Indian Institute of Science, Bangalore

    H. Ramesh

Authors
  1. V. S. Anil Kumar
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  2. Sunil Arya
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  3. H. Ramesh
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Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Ugo Montanari

  2. Center for Computer Sciences, University of Geneva, 24, Rue Général Dufour, 1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. Department of Computer Sciences, ETH Zurich, 8092, Zurich, Switzerland

    Emo Welzl

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© 2000 Springer-Verlag Berlin Heidelberg

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Kumar, V.S.A., Arya, S., Ramesh, H. (2000). Hardness of Set Cover with Intersection 1. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_53

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  • DOI: https://doi.org/10.1007/3-540-45022-X_53

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  • Print ISBN: 978-3-540-67715-4

  • Online ISBN: 978-3-540-45022-1

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