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Vikram SharmaEmail:
vikram at imsc dot res dot in |
Research Interests
- Computational Algebra
- Numerical Analysis
- Symbolic-Numeric Computation
Publications
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Thesis: Complexity Analysis of Algorithms in Algebraic Computation
Advisor: Prof. Chee Yap - Robust Approximate Zeros, with Zilin Du and Chee Yap. Appeared in ESA'05.
- Amortized Bound for Root Isolation Via Sturm Sequences, with Zilin Du and Chee Yap. Appeared in SNC'05.
- Almost Tight Recursion Tree Bounds for the Descartes Method, with Arno Eigenwillig and Chee Yap. Appeared in ISSAC 2006.
- Robust Approximate Zeros in Banach Space. Appeared in Mathematics in Computer Science.
- Complexity of Real Root Isolation Using Continued Fractions. Appeared in ISSAC 2007. Definitive version appears here in Theoretical Computer Science (TCS).
- Bounds on Absolute Positiveness of Multivariate Polynomials, with Prashant Batra. Published in JSC 2010.
- Robust Geometric Computation, with Chee Yap. Encyclopedia of Algorithms, 2008.
- Applications of Dimensionality Reduction and Exponential Sums to Graph Automorphism, with Madhusudan Manjunath. Theoretical Computer Science, 2011..
- Near Optimal Tree Size Bounds on a Simple Real Root Isolation Algorithm, with Chee Yap. In ISSAC, 2012
- Towards Exact Numerical Voronoi Diagrams, with Chee Yap and Jyh-Ming Lien. In International Symposium on Voronoi Diagrams (ISVD), 2012.
- Analytic Root Clustering: A Complete Algorithm using Soft Zero Tests, with Chee Yap and M. Sagraloff. Appeared in Computability in Europe (CiE2013), Milan, Italy, 2013.
- Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision, with Jyh-Ming Lien, Gert Vegter and Chee Yap. Inl. Cong. on Mathematical Softwares (ICMS), Seoul, 2014.
- Near Optimal Algorithms for Real Root Isolation, with P. Batra, in ISSAC, 2015. Journal version JSC, 2017.
- Complexity Analysis of Root Clustering for a Complex Polynomial, with R. Becker, M. Sagraloff, J. Xu, C. Yap in ISSAC, 2016.
- A Lower Bound for Computing Lagrange's Real Root Bound, with Swaroop N.P., in CASC, 2016.
- Improved Bounds on Absolute Positiveness of Multivariate Polynomials, with Swaroop N.P., ISSAC, 2017. Journal version JSC, 2019.
- Bounds on Distance to Variety in Terms of Coefficients of Bivariate Polynomials, arxiv. 2017.
- A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on Pellet Test and Newton Iteration, with R. Becker, M. Sagraloff, C. Yap. JSC, 2018.
- Complexity of a Root Clustering Algorithm, with P. Batra, CCA, 2018.
- Stronger Tradeoffs for Orthogonal Range Querying in the Semigroup Model, with Swaroop N.P., FSTTCS, 2018.
- Complexity of a root clustering algorithm for holomorphic functions, with P. Batra, Theoretical Computer Science, Vol 999. Complete version of the abstract appearing in CCA, 2018.
- Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case, ISSAC, 2020.
Education
- August 2001 - Oct. 2006
Ph. D. student in Computer Science at New York University, New York, USA. Thesis Advisor: Prof. Chee Yap. - August 1997 - May 2001
B.Tech. in Computer Science and Engineering from IT-BHU, Varanasi.
