A spectral approach to lower bounds with applications to geometric searching

SIAM Journal on Computing

Volumn 27, Issue 2, 1998, Pages 545-556

  Chazelle, Bernard ^a  

^a Princeton University   (United States)

Author keywords

Circuit complexity; Eigenvalues; Lower bounds; Range searching

Indexed keywords

EID: 0000006433     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794275665     Document Type: Article

References (20)

1. R. ALEXANDER, Geometric methods in the study of irregularities of distribution, Combinatorica, 10 (1990), pp. 115-136.
2. N. ALON, M. KARCHMER, AND A. WIGDERSON, Linear circuits over GF(2), SIAM J. Comput., 19 (1990), pp. 1064-1067.
3. A. AMIR, R. BEIGEL, AND W. GASARCH, Some connections between bounded query classes and nonuniform complexity, 5th Annual IEEE Structure in Complexity Theory Conference, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 232-243.
4. J. BECK AND W. W. L. CHEN, Irregularities of Distribution, Cambridge Tracts in Mathematics 89, Cambridge University Press, Cambridge, 1987.
5. R. B. BOPPANA AND M. SIPSER, The complexity of finite functions, in Handbook of Theoretical Computer Science, Vol. A, Algorithms and Complexity, MIT Press/Elsevier, Cambridge/New York, 1990, pp. 757-804.
6. J. Y. CAI, Lower bounds for constant depth circuits in the presence of help bits, in Proc. 30th Annual Symp. Foundation Comput. Sci., (FOCS), IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 532-537.
7. B. CHAZELLE, Lower bounds on the complexity of polytope range searching, J. Amer. Math. Soc., 2 (1989), pp. 637-666.
8. B. CHAZELLE, Geometric discrepancy revisited, in Proc. 34th Annual IEEE Symp. Foundation Comput. Sci., (FOCS), IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 392-399.
9. B. CHAZELLE, Computational geometry: A retrospective, in Computing in Euclidean Geometry, 2nd ed., D.-Z. Du and F. Hwang, eds., World Scientific Press, River Edge, NJ, 1995, pp. 22-46.
10. B. CHAZELLE, J. MATOUŠEK, AND M. SHARIR, An elementary approach to lower bounds in geometric discrepancy, Discrete Comput. Geom., 13 (1995), pp. 363-381.
11. M. L. FREDMAN, Lower bounds on the complexity of some optimal data structures, SIAM J. Comput., 10 (1981), pp. 1-10.
12. M. GRÖTSCHEL, L. LOVÁSZ, AND A. SCHRIJVER, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, New York, 1988.
13. J. VON ZUR GATHEN, Algebraic complexity theory, Ann. Rev. Comput. Sci., 1988, pp. 317-347.
14. P. LANCASTER AND M. TISMENETSKY, The Theory of Matrices, 2nd ed., Academic Press, New York, 1985.
15. J. MATOUŠEK, Range searching with efficient hierarchical cuttings, Discrete Comput. Geom., 10 (1993), pp. 157-182.
16. J. MATOUŠEK, Geometric range searching, Tech. Report B-93-09, Free Univ. Berlin, 1993.
17. K. MEHLHORN, Data Structures and Algorithms 3; Multidimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, 1984.
18. J. MORGENSTERN, Note on a lower bound of the linear complexity of the fast Fourier transform, J. ACM, 20 (1973), pp. 305-306.
19. K. MULMULEY, Computational Geometry: An Introduction Through Randomized Algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1994.
20. V. STRASSEN, Algebraic complexity theory, in Handbook of Theoretical Computer Science, Vol. A, Algorithms and Complexity, MIT Press/Elsevier, Cambridge/New York, 1990, pp. 633-672.