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A unified approach to approximation schemes for NP- and PSPACE-hard problems for geometric graphs

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Algorithms — ESA '94 (ESA 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

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Abstract

We present parallel approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner [CCJ90, MHR92, Te91]. Our NC-approximation schemes exhibit the same time versus performance trade-off as those of Baker [Ba83].

We also define the concept of λ-precision unit disk graphs and show that for such graphs our NC approximation schemes have better time versus performance trade-offs and several other graph problems have efficient approximation schemes.

Our parallel approximation schemes can also be extended to obtain efficient parallel approximation schemes for problems on unit disk graphs specified using a restricted version of the hierarchical specification language of Bentley, Ottmann and Widmayer [BOW83]. While we can show that many graph problems are PSPACE-hard even for this restricted form of specifications, nevertheless, these problems possess efficient approximation schemes.

Supported by NSF Grants CCR 89-03319 and CCR 90-06396.

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Authors and Affiliations

  1. Dept. of Computer Science, University at Albany-SUNY, 12222, Albany, NY

    H. B. Hunt III, S. S. Ravi, M. V. Marathe, D. J. Rosenkrantz, V. Radhakrishnan & R. E. Stearns

  2. Hewlett-Packard Company, 19447 Pruneridge Avenue, 95014, Cupertino, CA

    V. Radhakrishnan

Authors
  1. H. B. Hunt III
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  2. S. S. Ravi
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  3. M. V. Marathe
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  4. D. J. Rosenkrantz
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  5. V. Radhakrishnan
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  6. R. E. Stearns
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Hunt, H.B., Ravi, S.S., Marathe, M.V., Rosenkrantz, D.J., Radhakrishnan, V., Stearns, R.E. (1994). A unified approach to approximation schemes for NP- and PSPACE-hard problems for geometric graphs. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049428

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  • DOI: https://doi.org/10.1007/BFb0049428

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  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

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