Efficient Approximation Schemes for Geometric Problems?

  • Dániel Marx
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

An EPTAS (efficient PTAS) is an approximation scheme where ε does not appear in the exponent of n, i.e., the running time is f(ε)Open image in new windownc. We use parameterized complexity to investigate the possibility of improving the known approximation schemes for certain geometric problems to EPTAS. Answering an open question of Alber and Fiala [2], we show that Maximum Independent Set is W[1]-complete for the intersection graphs of unit disks and axis-parallel unit squares in the plane. A standard consequence of this result is that the \(n^{O(1/{\it \epsilon})}\) time PTAS of Hunt et al. [11] for Maximum Independent Set on unit disk graphs cannot be improved to an EPTAS. Similar results are obtained for the problem of covering points with squares.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dániel Marx
    • 1
  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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