Property Testing in Computational Geometry
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.
KeywordsComputational Geometry Delaunay Triangulation Geometric Object Query Complexity Property Testing
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- 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
- 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
- 11.O. Goldreich and D. Ron. Property testing in bounded degree graphs. In Proc. 29th ACM STOC, pp. 406–415, 1997.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