The combinatorial and topological complexity of a single cell

Discrete and Computational Geometry

Volumn 29, Issue 1, 2003, Pages 41-59

  Basu, Saugata ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038449007     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-002-2799-z     Document Type: Article

References (19)

1. P.K. Agarwal, M. Sharir, Arrangements and their applications, in Handbook of Computational Geometry, J.R. Sack, J. Urrutia (eds.), Elsevier, Amsterdam, 2000, pp. 49-120.
2. B. Aronov, M. Sharir, Castles in the air revisited, Discrete and Computational Geometry, 12 (1994), 119-150.
3. S. Basu, On bounding the Betti numbers and computing the Euler characteristics of semi-algebraic sets, Discrete & Computational Geometry, 22 (1999), 1-18.
4. S. Basu, On different bounds on different Betti numbers, Discrete & Computational Geometry, to appear. (Preliminary version in Proceedings of the ACM Symposium on Computational Geometry, pp. 288-292, 2001.) Available at www.math.gatech.edu/̃saugata/journalsocg01.ps.
5. S. Basu, R. Pollack, M.-F. Roy, On the combinatorial and algebraic complexity of Quantifier Elimination, Journal of the Association for Computing Machinery, 43 (1996), 1002-1045.
6. S. Basu, R. Pollack, M.-F. Roy, Computing roadmaps of semi-algebraic sets on a variety, Journal of the American Mathematical Society, 13 (2000), 55-82.
7. J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Springer-Verlag, Berlin, 1987.
8. M. Goresky, R. MacPherson, Stratified Morse Theory, Springer-Verlag, New York, 1987.
9. L.J. Guibas, M. Sharir, S. Sifrony, On the general motion planning problem with two degrees of freedom, Discrete & Computational Geometry, 4 (1989), 491-521.
10. D. Halperin, Arrangements, in Handbook of Discrete and Computational Geometry, J. O'Rourke, J.E. Goodman (eds.), CRC Press, Boca Raton, FL, 1997, pp. 389-412.
11. D. Halperin, M. Sharir, Almost tight upper bounds for the single cell and zone problems in three dimensions, Discrete & Computational Geometry, 14 (1995), 385-410.
12. D. Haussler, E. Welzl, Epsilon-nets and simplex range queries, Discrete & Computational Geometry, 2 (1987), 127-151.
13. P. MCMullen, The maximum number of faces of a convex polytope, Mathematika, 17(1970), 179-184.
14. J. Milnor, On the Betti numbers of real varieties, Proceedings of the American Mathematical Society, 15 (1964), 275-280.
15. O.A. Oleinik, I.B. Petrovsky, On the topology of real algebraic surfaces, Izvestiya Akademii Nauk SSSR, 13(1949), 389-402.
16. J. Pach, M. Sharir, The upper envelope of piecewise linear functions and the boundary of a region enclosed by convex plates: combinatorial analysis, Discrete & Computational Geometry, 4 (1989), 291-309.
17. B. Tagansky, A new technique for analyzing substructures in arrangements of piecewise linear surfaces, Discrete & Computational Geometry, 16 (1996), 455-479.
18. R. Thorn, Sur l'hornologie des variétés algébriques reelles, in Differential and Combinatorial Topology, S.S. Cairns (ed.), Princeton University Press, Princeton, NJ, 1965, pp. 255-265.
19. A. Wiernik, M. Sharir, Planar realization of nonlinear Davenport-Schinzel sequences by segments, Discrete & Computational Geometry, 3 (1988), 15-47.