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Bounding the radii of balls meeting every connected component of semi-algebraic sets
Saugata Basu
,
Marie-Françoise Roy
Journal Symbolic Computation
45
(12), 2010, pp. 1270-1279
An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions
Saugata Basu
,
Richard Pollack
,
Marie-Françoise Roy
Combinatorica
29
(5), 2009, pp. 523-546
Combinatorial complexity in
O
-minimal geometry
Saugata Basu
Proceedings of the 39th Annual ACM Symposium on Theory of Computing, STOC'2007 (San Diego, CA, USA, June 11-13, 2007)
, 2007, pp. 47-56
Computing the first few Betti numbers of semi-algebraic sets in single exponential time
Saugata Basu
Journal Symbolic Computation
41
(10), 2006, pp. 1125-1154
Computing the Betti numbers of arrangements in practice
Saugata Basu
,
Michael Kettner
Lecture Notes in Computer Science
3718
, 2005, pp. 13-31
Computing the first Betti number and the connected components of semi-algebraic sets
Saugata Basu
,
Richard Pollack
,
Marie-Françoise Roy
Proceedings of the 37th Annual ACM Symposium on Theory of Computing, STOC'2005 (Baltimore, Maryland, USA, May 22-24, 2005)
, 2005, pp. 304-312
Polynomial time algorithm for computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities
Saugata Basu
Proceedings of the 37th Annual ACM Symposium on Theory of Computing, STOC'2005 (Baltimore, Maryland, USA, May 22-24, 2005)
, 2005, pp. 313-322
On the realizable weaving patterns of polynomial curves in
R^3
Saugata Basu
,
Raghavan Dhandapani
,
Richard Pollack
Lecture Notes in Computer Science
3383
, 2004, pp. 36-42
Computing the Betti numbers of arrangements via spectral sequences
Saugata Basu
Journal of Computer and System Sciences
67
(2), 2003, pp. 244-262
Computing the Betty numbers of arrangements
Saugata Basu
Proceedings of the 34th Annual ACM Symposium on Theory of Computing, STOC'2002 (Montreal, Quebec, Canada, May 19-21, 2002)
, 2002, pp. 712-720
New results on quantifier elimination over real closed fields and applications to constraint databases
Saugata Basu
Journal of the ACM
46
(4), 1999, pp. 537-555
Complexity of computing semi-algebraic descriptions of the connected components of a semi-algebraic set
Saugata Basu
,
Richard Pollack
,
Marie-Françoise Roy
Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, ISSAC'98 (University of Rostock, Germany, August 13-15, 1998)
, 1998, pp. 25-29
A new algorithm to find a point in every cell defined by a family of polynomials
Saugata Basu
,
Richard Pollack
,
Marie-Françoise Roy
Texts and Monographs in Symbolic Computation
, 1998, pp. 341-350
On the combinatorial and topological complexity of a single cell
Saugata Basu
Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, FOCS'98 (Palo Alto, California, November 8-11, 1998)
, 1998, pp. 606-616
Computing roadmaps of semi-algebraic sets on a variety
Saugata Basu
,
Richard Pollack
,
Marie-Françoise Roy
Proceedings of the International Conference on Foundations of Computational Mathematics, FoCM'97 (Rio de Janeiro, Brazil, January 5-12, 1997)
, 1997, pp. 1-15
On computing a set of points meeting every cell defined by a family of polynomials on a variety
Saugata Basu
,
Richard Pollack
,
Marie-Françoise Roy
Journal of Complexity
13
(1), 1997, pp. 28-37
An improved algorithm for quantifier elimination over real closed fields
Saugata Basu
Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, FOCS'97 (Miami Beach, Florida, October 20-22, 1997)
, 1997, pp. 56-65
Uniform quantifier elimination and constraint query processing
Saugata Basu
Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, ISSAC'97 (Maui, Hawaii, July 21-23, 1997)
, 1997, pp. 21-27
On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets
Saugata Basu
Proceedings of the 28th Annual ACM Symposium on Theory of Computing (Philadelphia, Pennsylvania, May 22-24, 1996)
, 1996, pp. 408-417