Edit Profile (opens in new tab) Basu, Saugata Co-Author Distance Author ID: basu.saugata Published as: Basu, Saugata; Basu, S. Homepage: https://www.math.purdue.edu/~sbasu/ External Links: MGP · ResearchGate · dblp Videos: carmin.tv Documents Indexed: 104 Publications since 1994, including 2 Books and 10 Additional arXiv Preprints 4 Contributions as Editor · 1 Further Contribution Co-Authors: 56 Co-Authors with 82 Joint Publications 1,578 Co-Co-Authors all top 5 Co-Authors 21 single-authored 25 Roy, Marie-Françoise 20 Pollack, Richard M. 7 Riener, Cordian 6 Vorob’ëv, Nikolaĭ N. jun. 5 Gabrielov, Andrei 5 Parida, Laxmi 4 Karisani, Negin 4 Lerario, Antonio 4 Zell, Thierry 3 Barone, Sal 3 Kettner, Michael 3 Nezhad, Ali Mohammad 2 Cox, Nathanael 2 Natarajan, Abhiram 2 Pasechnik, Dmitrii V. 2 Patel, Deepam 2 Percival, Sarah 2 Utro, Filippo 1 Aronov, Boris 1 Bekka, Karim 1 Bhatnagar, Nayantara 1 Carrieri, Anna Paola 1 Chaudhuri, Parimal Pal 1 Roy Chowdhury, Dipanwita 1 Dhandapani, Raghavan 1 Fichou, Goulwen 1 Gonzalez-Vega, Laureano 1 Goodman, Jacob Eli 1 Gopalan, Parikshit 1 Guo, Shaoming 1 Guzmán-Sáenz, Aldo 1 Haiminen, Niina 1 Holmsen, Andreas F. 1 Isik, Umut 1 Khorasgani, Hamidreza Amini 1 Kuhn, David 1 Kummer, Mario Denis 1 Kurdyka, Krzysztof 1 Lipton, Richard Jay 1 Lundberg, Erik 1 Maji, Hemanta K. 1 Mandal, Sayan 1 Mangolte, Frédéric 1 Monnier, Jean-Philippe 1 Netzer, Tim 1 Nguyen, Hai H. 1 Pach, János 1 Perrucci, Daniel 1 Peterson, Chris 1 Powers, Victoria Ann 1 Quarez, Ronan 1 Raz, Orit E. 1 Rizzie, Anthony 1 Rolin, Jean-Philippe 1 Rosenblum, Alison 1 Safey El Din, Mohab 1 Schost, Éric 1 Sen Gupta, Indranil 1 Sharir, Micha 1 Sombra, Martín 1 Vinzant, Cynthia 1 Yorukoglu, Deniz 1 Zhang, Ruixiang 1 Zorin-Kranich, Pavel all top 5 Serials 12 Discrete & Computational Geometry 7 Foundations of Computational Mathematics 4 Proceedings of the London Mathematical Society. Third Series 4 Journal of the European Mathematical Society (JEMS) 3 Computational Complexity 3 SIAM Journal on Applied Algebra and Geometry 2 Advances in Mathematics 2 Mathematische Annalen 2 Journal of Symbolic Computation 2 Selecta Mathematica. New Series 2 Journal of the ACM 2 The Quarterly Journal of Mathematics 2 Algorithms and Computation in Mathematics 2 Forum of Mathematics, Sigma 2 Transactions of A. Razmadze Mathematical Institute 1 Acta Mechanica 1 IEEE Transactions on Computers 1 Journal of Algebra 1 Journal of Computer and System Sciences 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Mathematische Zeitschrift 1 Mathematika 1 Proceedings of the American Mathematical Society 1 Advances in Applied Mathematics 1 Combinatorica 1 Journal of Complexity 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Expositiones Mathematicae 1 Zapiski Nauchnykh Seminarov POMI 1 Oberwolfach Reports 1 Algorithms and Combinatorics 1 DIMACS. Series in Discrete Mathematics and Theoretical Computer Science 1 Panoramas et Synthèses 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Journal of Theoretical Biology all top 5 Fields 79 Algebraic geometry (14-XX) 56 Computer science (68-XX) 10 Mathematical logic and foundations (03-XX) 10 Convex and discrete geometry (52-XX) 9 Commutative algebra (13-XX) 9 Algebraic topology (55-XX) 5 General and overarching topics; collections (00-XX) 4 Combinatorics (05-XX) 4 Biology and other natural sciences (92-XX) 3 Field theory and polynomials (12-XX) 3 Functional analysis (46-XX) 3 Manifolds and cell complexes (57-XX) 3 Probability theory and stochastic processes (60-XX) 3 Operations research, mathematical programming (90-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Several complex variables and analytic spaces (32-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 85 Publications have been cited 1,340 times in 961 Documents Cited by ▼ Year ▼ Algorithms in real algebraic geometry. 2nd ed. Zbl 1102.14041 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 493 2006 Algorithms in real algebraic geometry. Zbl 1031.14028 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 210 2003 On the combinatorial and algebraic complexity of quantifier elimination. Zbl 0885.68070 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 117 1996 On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0973.14033 Basu, S. 37 1999 Computing roadmaps of semi-algebraic sets on a variety. Zbl 0933.14037 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 31 2000 Refined bounds on the number of connected components of sign conditions on a variety. Zbl 1250.14039 Barone, Sal; Basu, Saugata 27 2012 New results on quantifier elimination over real closed fields and applications to constraint databases. Zbl 1065.03507 Basu, Saugata 24 1999 A new algorithm to find a point in every cell defined by a family of polynomials. Zbl 0900.68278 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 21 1998 A baby step-giant step roadmap algorithm for general algebraic sets. Zbl 1322.14090 Basu, S.; Roy, M.-F.; Safey El Din, M.; Schost, É. 20 2014 On the number of cells defined by a family of polynomials on a variety. Zbl 0853.14028 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 18 1996 Computing the first few Betti numbers of semi-algebraic sets in single exponential time. Zbl 1126.14065 Basu, Saugata 17 2006 Divide and conquer roadmap for algebraic sets. Zbl 1329.14109 Basu, Saugata; Roy, Marie-Françoise 13 2014 Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions. Zbl 1332.13017 Basu, Saugata; Sombra, Martín 13 2016 Different bounds on the different Betti numbers of semi-algebraic sets. Zbl 1073.14556 Basu, Saugata 12 2003 Design of CAECC – cellular automata based error correcting code. Zbl 1068.68673 Chowdhury, Dipanwita Roy; Basu, Saugata; Gupta, Indranil Sen; Chaudhuri, Parimal Pal 12 1994 Polynomial hierarchy, Betti numbers, and a real analogue of Toda’s theorem. Zbl 1200.14108 Basu, Saugata; Zell, Thierry 11 2010 Computing the first Betti number of a semi-algebraic set. Zbl 1142.14036 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 11 2008 On computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0872.68050 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 11 1997 Betti number bounds, applications and algorithms. Zbl 1097.68152 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 10 2005 Computing the top Betti numbers of semialgebraic sets defined by quadratic inequalities in polynomial time. Zbl 1141.14034 Basu, Saugata 10 2008 Computing roadmaps of semi-algebraic sets. (Extended abstract). Zbl 0917.14028 Basu, S.; Pollack, R.; Roy, M.-F. 10 1996 On the Betti numbers of sign conditions. Zbl 1080.14068 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 10 2005 Algorithms in real algebraic geometry: a survey. Zbl 1398.14062 Basu, Saugata 10 2017 Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1218.14050 Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise 9 2010 On a real analog of Bézout inequality and the number of connected components of sign conditions. Zbl 1347.14010 Barone, Sal; Basu, Saugata 9 2016 On the number of homotopy types of fibres of a definable map. Zbl 1131.14060 Basu, Saugata; Vorobjov, Nicolai 9 2007 Algorithmic semi-algebraic geometry and topology – recent progress and open problems. Zbl 1145.14044 Basu, Saugata 9 2008 Bounding the radii of balls meeting every connected component of semi-algebraic sets. Zbl 1200.14107 Basu, Saugata; Roy, Marie-Françoise 8 2010 Random fields and the enumerative geometry of lines on real and complex hypersurfaces. Zbl 1423.14303 Basu, Saugata; Lerario, Antonio; Lundberg, Erik; Peterson, Chris 8 2019 A sharper estimate on the Betti numbers of sets defined by quadratic inequalities. Zbl 1185.14051 Basu, Saugata; Kettner, Michael 7 2008 Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Zbl 1423.14331 Basu, Saugata; Riener, Cordian 6 2017 Semi-monotone sets. Zbl 1284.14081 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 6 2013 Combinatorial complexity in o-minimal geometry. Zbl 1186.52017 Basu, Saugata 6 2010 Computing the first Betti number and the connected components of semi-algebraic sets. Zbl 1192.14003 Basu, Saugata; Pollack, Richard; Roy, Marie-Francoise 5 2005 On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0917.14029 Basu, Saugata 5 1996 Monotone functions and maps. Zbl 1273.14123 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 5 2013 Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1171.14040 Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise 5 2009 Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets. Zbl 1497.14117 Basu, Saugata; Riener, Cordian 5 2022 Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities. Zbl 1103.14032 Basu, Saugata 4 2006 An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions. Zbl 1212.14005 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 4 2009 A complex analogue of Toda’s theorem. Zbl 1268.14016 Basu, Saugata 4 2012 A complexity theory of constructible functions and sheaves. Zbl 1349.68098 Basu, Saugata 4 2015 An o-minimal Szemerédi-Trotter theorem. Zbl 1522.03138 Basu, Saugata; Raz, Orit E. 4 2018 Complexity of computing semi-algebraic descriptions of the connected components of a semialgebraic set. Zbl 0960.14033 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 4 1998 Computing the Euler-Poincaré characteristics of sign conditions. Zbl 1077.14086 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 4 2005 Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Zbl 1390.14175 Basu, Saugata; Riener, Cordian 4 2017 Spectral sequences, exact couples and persistent homology of filtrations. Zbl 1381.55009 Basu, Saugata; Parida, Laxmi 4 2017 Topological signatures for population admixture. Zbl 1355.92077 Parida, Laxmi; Utro, Filippo; Yorukoglu, Deniz; Carrieri, Anna; Kuhn, David; Basu, Saugata 3 2015 On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities. Zbl 1453.14143 Basu, Saugata; Riener, Cordian 3 2020 Polynomials that sign represent parity and Descartes’ rule of signs. Zbl 1188.68150 Basu, Saugata; Bhatnagar, Nayantara; Gopalan, Parikshit; Lipton, Richard J. 3 2008 Discrete and computational geometry. The Goodman-Pollack Festschrift. Zbl 1014.00040 3 2003 Combinatorial complexity in O-minimal geometry. Zbl 1232.68162 Basu, Saugata 3 2007 Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium. Zbl 1390.74147 Karan, S.; Basu, S.; Mandal, S. C. 3 2018 Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications. Zbl 1401.14228 Basu, Saugata; Rizzie, Anthony 3 2018 The Hadwiger transversal theorem for pseudolines. Zbl 1112.52001 Basu, Saugata; Goodman, Jacob E.; Holmsen, Andreas; Pollack, Richard 2 2005 The combinatorial and topological complexity of a single cell. Zbl 1017.68056 Basu, Saugata 2 2003 Algorithmic and quantitative real algebraic geometry. Proceedings of the DIMACS workshop on algorithmic and quantitative aspects of real algebraic geometry in mathematics and computer science, DIMACS Center, March 12–16, 2001. Zbl 1015.00018 2 2003 Computing the dimension of a semi-algebraic set. Zbl 1075.14053 Basu, S.; Pollack, R.; Roy, M.-F. 2 2004 Hausdorff approximations and volume of tubes of singular algebraic sets. Zbl 1537.14078 Basu, Saugata; Lerario, Antonio 2 2023 Computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0829.14025 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 2 1995 Substrate stiffness and mechanical stress due to intercellular cooperativity guides tissue structure. Zbl 1406.92045 Basu, S.; Sutradhar, S.; Paul, R. 2 2018 VC density of definable families over valued fields. Zbl 1495.14089 Basu, Saugata; Patel, Deepam 2 2021 Zeroes of polynomials on definable hypersurfaces: pathologies exist, but they are rare. Zbl 1467.14143 Basu, Saugata; Lerario, Antonio; Natarajan, Abhiram 2 2019 Computing the Betti numbers of arrangements in practice. Zbl 1169.68637 Basu, Saugata; Kettner, Michael 1 2005 Polynomial time algorithm for computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities. Zbl 1192.14002 Basu, Saugata 1 2005 Triangulations of monotone families. I: two-dimensional families. Zbl 1348.14134 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 1 2015 Different bounds on the different Betti numbers of semi-algebraic sets. Zbl 1375.14191 Basu, Saugata 1 2001 Real algebraic geometry. Zbl 1375.14006 1 2017 Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda’s theorem. Zbl 1456.14024 Basu, Saugata; Patel, Deepam 1 2020 On projections of semi-algebraic sets defined by few quadratic inequalities. Zbl 1137.14042 Basu, Saugata; Zell, Thierry 1 2008 Uniform quantifier elimination and constraint query processing. Zbl 0915.03031 Basu, Saugata 1 1997 Computing the Betti numbers of arrangements via spectral sequences. Zbl 1160.68606 Basu, Saugata 1 2003 A Helly-type theorem for semi-monotone sets and monotone maps. Zbl 1284.14082 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 1 2013 On projections of semi-algebraic sets defined by few quadratic inequalities. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.14095 Basu, Saugata; Zell, Thierry 1 2009 On the number of topological types occurring in a parameterized family of arrangements. Zbl 1159.52024 Basu, Saugata 1 2008 Bounding the number of stable homotopy types of a parametrized family of semi-algebraic sets defined by quadratic inequalities. Zbl 1193.14072 Basu, Saugata; Kettner, Michael 1 2009 On the realizable weaving patterns of polynomial curves in \(\mathbb R^3\). Zbl 1111.68721 Basu, Saugata; Dhandapani, Raghavan; Pollack, Richard 1 2005 Efficient simplicial replacement of semialgebraic sets. Zbl 1516.14106 Basu, Saugata; Karisani, Negin 1 2023 Essential simplices in persistent homology and subtle admixture detection. Zbl 1494.92095 Basu, Saugata; Utro, Filippo; Parida, Laxmi 1 2018 On the Reeb spaces of definable maps. Zbl 1500.03014 Basu, Saugata; Cox, Nathanael; Percival, Sarah 1 2022 A topological data analysis approach on predicting phenotypes from gene expression data. Zbl 1500.92079 Mandal, Sayan; Guzmán-Sáenz, Aldo; Haiminen, Niina; Basu, Saugata; Parida, Laxmi 1 2020 On the central path of semidefinite optimization: degree and worst-case convergence rate. Zbl 1490.14093 Basu, Saugata; Mohammad-Nezhad, Ali 1 2022 Persistent homology of semialgebraic sets. Zbl 1536.55005 Basu, Saugata; Karisani, Negin 1 2023 Abstract formulations of some theorems on nonmeasurable sets. Zbl 1428.28002 Basu, S.; Sen, D. 1 2017 On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms. Zbl 1397.14037 Basu, Saugata; Riener, Cordian 1 2018 Hausdorff approximations and volume of tubes of singular algebraic sets. Zbl 1537.14078 Basu, Saugata; Lerario, Antonio 2 2023 Efficient simplicial replacement of semialgebraic sets. Zbl 1516.14106 Basu, Saugata; Karisani, Negin 1 2023 Persistent homology of semialgebraic sets. Zbl 1536.55005 Basu, Saugata; Karisani, Negin 1 2023 Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets. Zbl 1497.14117 Basu, Saugata; Riener, Cordian 5 2022 On the Reeb spaces of definable maps. Zbl 1500.03014 Basu, Saugata; Cox, Nathanael; Percival, Sarah 1 2022 On the central path of semidefinite optimization: degree and worst-case convergence rate. Zbl 1490.14093 Basu, Saugata; Mohammad-Nezhad, Ali 1 2022 VC density of definable families over valued fields. Zbl 1495.14089 Basu, Saugata; Patel, Deepam 2 2021 On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities. Zbl 1453.14143 Basu, Saugata; Riener, Cordian 3 2020 Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda’s theorem. Zbl 1456.14024 Basu, Saugata; Patel, Deepam 1 2020 A topological data analysis approach on predicting phenotypes from gene expression data. Zbl 1500.92079 Mandal, Sayan; Guzmán-Sáenz, Aldo; Haiminen, Niina; Basu, Saugata; Parida, Laxmi 1 2020 Random fields and the enumerative geometry of lines on real and complex hypersurfaces. Zbl 1423.14303 Basu, Saugata; Lerario, Antonio; Lundberg, Erik; Peterson, Chris 8 2019 Zeroes of polynomials on definable hypersurfaces: pathologies exist, but they are rare. Zbl 1467.14143 Basu, Saugata; Lerario, Antonio; Natarajan, Abhiram 2 2019 An o-minimal Szemerédi-Trotter theorem. Zbl 1522.03138 Basu, Saugata; Raz, Orit E. 4 2018 Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium. Zbl 1390.74147 Karan, S.; Basu, S.; Mandal, S. C. 3 2018 Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications. Zbl 1401.14228 Basu, Saugata; Rizzie, Anthony 3 2018 Substrate stiffness and mechanical stress due to intercellular cooperativity guides tissue structure. Zbl 1406.92045 Basu, S.; Sutradhar, S.; Paul, R. 2 2018 Essential simplices in persistent homology and subtle admixture detection. Zbl 1494.92095 Basu, Saugata; Utro, Filippo; Parida, Laxmi 1 2018 On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms. Zbl 1397.14037 Basu, Saugata; Riener, Cordian 1 2018 Algorithms in real algebraic geometry: a survey. Zbl 1398.14062 Basu, Saugata 10 2017 Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Zbl 1423.14331 Basu, Saugata; Riener, Cordian 6 2017 Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Zbl 1390.14175 Basu, Saugata; Riener, Cordian 4 2017 Spectral sequences, exact couples and persistent homology of filtrations. Zbl 1381.55009 Basu, Saugata; Parida, Laxmi 4 2017 Real algebraic geometry. Zbl 1375.14006 1 2017 Abstract formulations of some theorems on nonmeasurable sets. Zbl 1428.28002 Basu, S.; Sen, D. 1 2017 Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions. Zbl 1332.13017 Basu, Saugata; Sombra, Martín 13 2016 On a real analog of Bézout inequality and the number of connected components of sign conditions. Zbl 1347.14010 Barone, Sal; Basu, Saugata 9 2016 A complexity theory of constructible functions and sheaves. Zbl 1349.68098 Basu, Saugata 4 2015 Topological signatures for population admixture. Zbl 1355.92077 Parida, Laxmi; Utro, Filippo; Yorukoglu, Deniz; Carrieri, Anna; Kuhn, David; Basu, Saugata 3 2015 Triangulations of monotone families. I: two-dimensional families. Zbl 1348.14134 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 1 2015 A baby step-giant step roadmap algorithm for general algebraic sets. Zbl 1322.14090 Basu, S.; Roy, M.-F.; Safey El Din, M.; Schost, É. 20 2014 Divide and conquer roadmap for algebraic sets. Zbl 1329.14109 Basu, Saugata; Roy, Marie-Françoise 13 2014 Semi-monotone sets. Zbl 1284.14081 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 6 2013 Monotone functions and maps. Zbl 1273.14123 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 5 2013 A Helly-type theorem for semi-monotone sets and monotone maps. Zbl 1284.14082 Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai 1 2013 Refined bounds on the number of connected components of sign conditions on a variety. Zbl 1250.14039 Barone, Sal; Basu, Saugata 27 2012 A complex analogue of Toda’s theorem. Zbl 1268.14016 Basu, Saugata 4 2012 Polynomial hierarchy, Betti numbers, and a real analogue of Toda’s theorem. Zbl 1200.14108 Basu, Saugata; Zell, Thierry 11 2010 Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1218.14050 Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise 9 2010 Bounding the radii of balls meeting every connected component of semi-algebraic sets. Zbl 1200.14107 Basu, Saugata; Roy, Marie-Françoise 8 2010 Combinatorial complexity in o-minimal geometry. Zbl 1186.52017 Basu, Saugata 6 2010 Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1171.14040 Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise 5 2009 An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions. Zbl 1212.14005 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 4 2009 On projections of semi-algebraic sets defined by few quadratic inequalities. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.14095 Basu, Saugata; Zell, Thierry 1 2009 Bounding the number of stable homotopy types of a parametrized family of semi-algebraic sets defined by quadratic inequalities. Zbl 1193.14072 Basu, Saugata; Kettner, Michael 1 2009 Computing the first Betti number of a semi-algebraic set. Zbl 1142.14036 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 11 2008 Computing the top Betti numbers of semialgebraic sets defined by quadratic inequalities in polynomial time. Zbl 1141.14034 Basu, Saugata 10 2008 Algorithmic semi-algebraic geometry and topology – recent progress and open problems. Zbl 1145.14044 Basu, Saugata 9 2008 A sharper estimate on the Betti numbers of sets defined by quadratic inequalities. Zbl 1185.14051 Basu, Saugata; Kettner, Michael 7 2008 Polynomials that sign represent parity and Descartes’ rule of signs. Zbl 1188.68150 Basu, Saugata; Bhatnagar, Nayantara; Gopalan, Parikshit; Lipton, Richard J. 3 2008 On projections of semi-algebraic sets defined by few quadratic inequalities. Zbl 1137.14042 Basu, Saugata; Zell, Thierry 1 2008 On the number of topological types occurring in a parameterized family of arrangements. Zbl 1159.52024 Basu, Saugata 1 2008 On the number of homotopy types of fibres of a definable map. Zbl 1131.14060 Basu, Saugata; Vorobjov, Nicolai 9 2007 Combinatorial complexity in O-minimal geometry. Zbl 1232.68162 Basu, Saugata 3 2007 Algorithms in real algebraic geometry. 2nd ed. Zbl 1102.14041 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 493 2006 Computing the first few Betti numbers of semi-algebraic sets in single exponential time. Zbl 1126.14065 Basu, Saugata 17 2006 Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities. Zbl 1103.14032 Basu, Saugata 4 2006 Betti number bounds, applications and algorithms. Zbl 1097.68152 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 10 2005 On the Betti numbers of sign conditions. Zbl 1080.14068 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 10 2005 Computing the first Betti number and the connected components of semi-algebraic sets. Zbl 1192.14003 Basu, Saugata; Pollack, Richard; Roy, Marie-Francoise 5 2005 Computing the Euler-Poincaré characteristics of sign conditions. Zbl 1077.14086 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 4 2005 The Hadwiger transversal theorem for pseudolines. Zbl 1112.52001 Basu, Saugata; Goodman, Jacob E.; Holmsen, Andreas; Pollack, Richard 2 2005 Computing the Betti numbers of arrangements in practice. Zbl 1169.68637 Basu, Saugata; Kettner, Michael 1 2005 Polynomial time algorithm for computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities. Zbl 1192.14002 Basu, Saugata 1 2005 On the realizable weaving patterns of polynomial curves in \(\mathbb R^3\). Zbl 1111.68721 Basu, Saugata; Dhandapani, Raghavan; Pollack, Richard 1 2005 Computing the dimension of a semi-algebraic set. Zbl 1075.14053 Basu, S.; Pollack, R.; Roy, M.-F. 2 2004 Algorithms in real algebraic geometry. Zbl 1031.14028 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 210 2003 Different bounds on the different Betti numbers of semi-algebraic sets. Zbl 1073.14556 Basu, Saugata 12 2003 Discrete and computational geometry. The Goodman-Pollack Festschrift. Zbl 1014.00040 3 2003 The combinatorial and topological complexity of a single cell. Zbl 1017.68056 Basu, Saugata 2 2003 Algorithmic and quantitative real algebraic geometry. Proceedings of the DIMACS workshop on algorithmic and quantitative aspects of real algebraic geometry in mathematics and computer science, DIMACS Center, March 12–16, 2001. Zbl 1015.00018 2 2003 Computing the Betti numbers of arrangements via spectral sequences. Zbl 1160.68606 Basu, Saugata 1 2003 Different bounds on the different Betti numbers of semi-algebraic sets. Zbl 1375.14191 Basu, Saugata 1 2001 Computing roadmaps of semi-algebraic sets on a variety. Zbl 0933.14037 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 31 2000 On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0973.14033 Basu, S. 37 1999 New results on quantifier elimination over real closed fields and applications to constraint databases. Zbl 1065.03507 Basu, Saugata 24 1999 A new algorithm to find a point in every cell defined by a family of polynomials. Zbl 0900.68278 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 21 1998 Complexity of computing semi-algebraic descriptions of the connected components of a semialgebraic set. Zbl 0960.14033 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 4 1998 On computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0872.68050 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 11 1997 Uniform quantifier elimination and constraint query processing. Zbl 0915.03031 Basu, Saugata 1 1997 On the combinatorial and algebraic complexity of quantifier elimination. Zbl 0885.68070 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 117 1996 On the number of cells defined by a family of polynomials on a variety. Zbl 0853.14028 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 18 1996 Computing roadmaps of semi-algebraic sets. (Extended abstract). Zbl 0917.14028 Basu, S.; Pollack, R.; Roy, M.-F. 10 1996 On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0917.14029 Basu, Saugata 5 1996 Computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0829.14025 Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise 2 1995 Design of CAECC – cellular automata based error correcting code. Zbl 1068.68673 Chowdhury, Dipanwita Roy; Basu, Saugata; Gupta, Indranil Sen; Chaudhuri, Parimal Pal 12 1994 all cited Publications top 5 cited Publications all top 5 Cited by 1,268 Authors 48 Basu, Saugata 39 Safey El Din, Mohab 23 Roy, Marie-Françoise 18 Sharir, Micha 16 Rouillier, Fabrice 14 Sagraloff, Michael 14 Zahl, Joshua 13 Pach, János 13 Perrucci, Daniel 13 Riener, Cordian 12 Mourrain, Bernard 12 Tsigaridas, Elias P. 11 Heintz, Joos 11 Lerario, Antonio 11 Schost, Éric 10 Fox, Jacob 10 Gonzalez-Vega, Laureano 10 Moreno Maza, Marc 10 Rojas, J. Maurice 10 Zeng, Guangxing 9 Davenport, James Harold 9 Henrion, Didier 9 Hong, Hoon 9 Jeronimo, Gabriela 9 Xia, Bican 8 Alcazar, Juan Gerardo 8 Bank, Bernd 8 Batkhin, Alexandr B. 8 Chen, Changbo 8 Cucker, Felipe 8 Giusti, Marc 8 Koiran, Pascal 8 Moroz, Guillaume 8 Xiao, ShuiJing 7 Aronov, Boris 7 Binyamini, Gal 7 Cheng, Jinsan 7 Diatta, Daouda Niang 7 Díaz-Toca, Gema María 7 Ezra, Esther E. 7 Kerber, Michael 7 Miltzow, Tillmann 7 Pollack, Richard M. 7 Pouget, Marc 7 Sabia, Juan 7 Sheffer, Adam 7 Vorob’ëv, Nikolaĭ N. jun. 6 Bouzidi, Yacine 6 Bürgisser, Peter 6 Caravantes, Jorge 6 de Wolff, Timo 6 Emiris, Ioannis Z. 6 England, Matthew 6 Feliu, Elisenda 6 Hauenstein, Jonathan D. 6 Lasserre, Jean-Bernard 6 Lazard, Sylvain 6 Magron, Victor 6 Mateus, Paulo C. 6 Matoušek, Jiří 6 Naldi, Simone 6 Pardo, Luis Miguel 6 Strzeboński, Adam Wojciech 6 Sturm, Thomas 6 Wu, Wenyuan 6 Yap, Chee-Keng 5 Berberich, Eric 5 Bukh, Boris 5 Drusvyatskiy, Dmitriy 5 Fortuna, Elisabetta 5 Gianni, Patrizia M. 5 Gortler, Steven J. 5 Joswig, Michael 5 Kuijpers, Bart H. M. 5 Scheiblechner, Peter 5 Sottile, Frank 5 Starchenko, Sergei 5 Subramani, Krishnan 5 Xu, Ming 5 Ziegler, Martin 4 Ábrahám, Erika 4 Agarwal, Pankaj Kumar 4 Amidou, Morou 4 Anai, Hirokazu 4 Bihan, Frédéric 4 Bourgain, Jean 4 Brown, Christopher W. 4 Chernikov, Artem 4 Choudhury, Pabitra Pal 4 Drton, Mathias 4 Eirinakis, Pavlos 4 Gabrielov, Andrei 4 Grigor’ev, Dmitriĭ Yur’evich 4 Grimson, Rafael 4 Hansen, Kristoffer Arnsfelt 4 Har-Peled, Sariel 4 Jin, Kai 4 Kaplan, Haim 4 Kurdyka, Krzysztof 4 Meer, Klaus ...and 1,168 more Authors all top 5 Cited in 234 Serials 96 Journal of Symbolic Computation 60 Discrete & Computational Geometry 31 Theoretical Computer Science 25 Journal of Complexity 22 Foundations of Computational Mathematics 15 Computational Geometry 14 Computer Aided Geometric Design 12 Mathematical Programming. Series A. 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Theory and Methods 2 International Journal of Computer Mathematics 2 Archive for Mathematical Logic 2 Journal de Théorie des Nombres de Bordeaux 2 Advances in Computational Mathematics ...and 134 more Serials all top 5 Cited in 56 Fields 436 Computer science (68-XX) 346 Algebraic geometry (14-XX) 136 Numerical analysis (65-XX) 123 Mathematical logic and foundations (03-XX) 114 Commutative algebra (13-XX) 90 Convex and discrete geometry (52-XX) 86 Operations research, mathematical programming (90-XX) 84 Combinatorics (05-XX) 77 Field theory and polynomials (12-XX) 46 Number theory (11-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 30 Real functions (26-XX) 30 Quantum theory (81-XX) 26 Dynamical systems and ergodic theory (37-XX) 26 Algebraic topology (55-XX) 25 Biology and other natural sciences (92-XX) 21 Probability theory and stochastic processes (60-XX) 21 Statistics (62-XX) 21 Systems theory; control (93-XX) 20 Several complex variables and analytic spaces (32-XX) 20 Ordinary differential equations (34-XX) 18 Geometry (51-XX) 16 Functions of a complex variable (30-XX) 16 Operator theory (47-XX) 14 Group theory and generalizations (20-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Information and communication theory, circuits (94-XX) 11 Partial differential equations (35-XX) 11 Differential geometry (53-XX) 11 Manifolds and cell complexes (57-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Approximations and expansions (41-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Mechanics of particles and systems (70-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 Special functions (33-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 General topology (54-XX) 6 Topological groups, Lie groups (22-XX) 6 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 4 Associative rings and algebras (16-XX) 3 Difference and functional equations (39-XX) 2 History and biography (01-XX) 2 General algebraic systems (08-XX) 2 Measure and integration (28-XX) 2 Abstract harmonic analysis (43-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Fluid mechanics (76-XX) 1 Mathematics education (97-XX) Citations by Year