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Property Testing in Computational Geometry

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Algorithms - ESA 2000 (ESA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1879))

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Abstract

We consider the notion of property testing as applied to computational geometry. We aim at developing efficient algorithms which determine whether a given (geometrical) object has a predetermined property Q or is “far” from any object having the property. We show that many basic geometric properties have very efficient testing algorithms, whose running time is significantly smaller than the object description size.

Research supported in part by DFG Grant Me872/7-1.

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References

  1. N. Alon, E. Fischer, M. Krivelevich, and M. Szegedy. Efficient testing of large graphs. In Proc. 40th IEEE FOCS, pp. 656–666, 1999.

    Google Scholar 

  2. N. Alon, M. Krivelevich, I. Newman, and M. Szegedy. Regular languages are testable with a constant number of queries. In Proc. 40th IEEE FOCS, pp. 645–655, 1999.

    Google Scholar 

  3. H. Alt, R. Fleischer, M. Kaufmann, K. Mehlhorn, S. Näher, S. Schirra, and C. Uhrig. Algorithmica, 8(5/6):365–389, 1992.

    MathSciNet  Google Scholar 

  4. M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. Journal of Computer and System Sciences, 47(3):549–595, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  5. T. M. Chan. Output-sensitive results on convex hulls, extreme points, and related problems. Discrete & Computational Geometry, 16:369–387, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Dyer and N. Megiddo. Linear programming in low dimensions. In J. E. Goodman and J. O’Rourke, eds., Handbook of Discrete and Computational Geometry, ch. 38, pp. 699–710, CRC Press, Boca Raton, FL, 1997.

    Google Scholar 

  7. F. Ergün, S. Kannan, S. Ravi Kumar, R. Rubinfeld, and M. Viswanathan. Spot-checkers. In Proc. 30th ACM STOC, pp. 259–268, 1998.

    Google Scholar 

  8. F. Ergün, S. Ravi Kumar, and R. Rubinfeld. Approximate checking of polynomials and functional equations. In Proc. 37th IEEE FOCS, pp. 592–601, 1996.

    Google Scholar 

  9. O. Goldreich, S. Goldwasser, E. Lehman, and D. Ron. Testing monotonicity. In Proc. 39th IEEE FOCS, pp. 426–435, 1998.

    Google Scholar 

  10. O. Goldreich, S. Goldwasser, and D. Ron. Property testing and its connection to learning and approximation. Journal of the ACM, 45(4):653–750, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  11. O. Goldreich and D. Ron. Property testing in bounded degree graphs. In Proc. 29th ACM STOC, pp. 406–415, 1997.

    Google Scholar 

  12. O. Goldreich and D. Ron. A sublinear bipartiteness tester for bounded degree graphs. Combinatorica, 19(3):335–373, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Haussler and E. Welzl. Epsilon-nets and simplex range queries. Discrete & Computational Geometry, 2:127–151, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  14. K. Mehlhorn, S. Näher, M. Seel, R. Seidel, T. Schilz, S. Schirra, and C. Uhrig. Checking geometric programs or verification of geometric structures. Computational Geometry: Theory and Applications, 12:85–103, 1999.

    MATH  MathSciNet  Google Scholar 

  15. R. Rubinfeld and M. Sudan. Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing, 25(2):252–271, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  16. R. Rubinfeld. Robust functional equations and their applications to program testing. In Proc. 35th IEEE FOCS, pp. 288–299, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, New Jersey Institute of Technology, Newark, NJ, 07102-1982, USA

    Artur Czumaj

  2. Heinz Nixdorf Institute and Department of Mathematics & Computer Science, University of Paderborn, D-33095, Paderborn, Germany

    Christian Sohler & Martin Ziegler

Authors
  1. Artur Czumaj
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  2. Christian Sohler
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  3. Martin Ziegler
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Mike S. Paterson

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© 2000 Springer-Verlag Berlin Heidelberg

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Czumaj, A., Sohler, C., Ziegler, M. (2000). Property Testing in Computational Geometry. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_15

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  • DOI: https://doi.org/10.1007/3-540-45253-2_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41004-1

  • Online ISBN: 978-3-540-45253-9

  • eBook Packages: Springer Book Archive

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