Narendra Krishna Karmarkar (born circa 1956) is an Indian mathematician. Karmarkar developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher.[2]
Narendra Krishna Karmarkar | |
|---|---|
| Born | 1956 (age 67–68) Gwalior, Madhya Pradesh, India |
| Alma mater | IIT Bombay (BTech) California Institute of Technology (MS) University of California, Berkeley (PhD) |
| Known for | Karmarkar's algorithm |
| Scientific career | |
| Fields | Mathematics, computing science |
| Institutions | Bell Labs |
| Thesis | Coping with NP-Hard Problems (1983) |
| Doctoral advisor | Richard M. Karp[1] |
He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method. The algorithm is a cornerstone in the field of linear programming. He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey.
Biography
editKarmarkar received his B.Tech in Electrical Engineering from IIT Bombay in 1978, M.S. from the California Institute of Technology in 1979,[3] and Ph.D. in Computer Science from the University of California, Berkeley in 1983 under the supervision of Richard M. Karp.[4] Karmarkar was a post-doctoral research fellow at IBM research (1983), Member of Technical Staff and fellow at Mathematical Sciences Research Center, AT&T Bell Laboratories (1983–1998), professor of mathematics at M.I.T. (1991), at Institute for Advanced study, Princeton (1996), and Homi Bhabha Chair Professor at the Tata Institute of Fundamental Research in Mumbai from 1998 to 2005. He was the scientific advisor to the chairman of the TATA group (2006–2007). During this time, he was funded by Ratan Tata to scale-up the supercomputer he had designed and prototyped at TIFR. The scaled-up model ranked ahead of supercomputer in Japan at that time and achieved the best ranking India ever achieved in supercomputing. He was the founding director of Computational Research labs in Pune, where the scaling-up work was performed. He continues to work on his new architecture for supercomputing.
Work
editKarmarkar's algorithm
editKarmarkar's algorithm solves linear programming problems in polynomial time. These problems are represented by a number of linear constraints involving a number of variables. The previous method of solving these problems consisted of considering the problem as a high-dimensional solid with vertices, where the solution was approached by traversing from vertex to vertex. Karmarkar's novel method approaches the solution by cutting through the above solid in its traversal. Consequently, complex optimization problems are solved much faster using the Karmarkar's algorithm. A practical example of this efficiency is the solution to a complex problem in communications network optimization, where the solution time was reduced from weeks to days. His algorithm thus enables faster business and policy decisions. Karmarkar's algorithm has stimulated the development of several interior-point methods, some of which are used in current implementations of linear-program solvers.
Galois geometry
editAfter working on the interior-point method, Karmarkar worked on a new architecture for supercomputing, based on concepts from finite geometry, especially projective geometry over finite fields.[5][6][7][8]
Awards
edit- The Association for Computing Machinery awarded him the prestigious Paris Kanellakis Award in 2000 for his work on polynomial-time interior-point methods for linear programming for "specific theoretical accomplishments that have had a significant and demonstrable effect on the practice of computing".
- Srinivasa Ramanujan Birth Centenary Award for 1999, presented by the Prime Minister of India.
- Distinguished Alumnus Award, Indian Institute of Technology, Bombay, 1996.
- Distinguished Alumnus Award, Computer Science and Engineering, University of California, Berkeley (1993).
- Fulkerson Prize in Discrete Mathematics given jointly by the American Mathematical Society & Mathematical Programming Society (1988)
- Fellow of Bell Laboratories (since 1987).
- Texas Instruments Founders' Prize (1986).
- Marconi International Young Scientist Award (1985).
- Golden Plate Award of the American Academy of Achievement, presented by former U.S. president (1985).[9][10]
- Frederick W. Lanchester Prize of the Operations Research Society of America for the Best Published Contributions to Operations Research (1984).
- President of India gold medal, I.I.T. Bombay (1978).
References
edit- ^ Narendra Karmarkar at the Mathematics Genealogy Project.
- ^ Thomson ISI. "Karmarkar, Narendra K., ISI Highly Cited Researchers". Archived from the original on 23 March 2006. Retrieved 20 June 2009.
- ^ "Eighty-Fifth Annual Commencement" (PDF). California Institute of Technology. 8 June 1979. p. 13.
- ^ Narendra Karmarkar at the Mathematics Genealogy Project
- ^ Karmarkar, Narendra (1991). "A new parallel architecture for sparse matrix computation based on finite projective geometries". Proceedings of the 1991 ACM/IEEE conference on Supercomputing – Supercomputing '91. pp. 358–369. doi:10.1145/125826.126029. ISBN 0897914597. S2CID 6665759.
- ^ Karmarkar, N. K., Ramakrishnan, K. G. "Computational results of an interior point algorithm for large scale linear programming". Mathematical Programming. 52: 555–586 (1991).
- ^ Amruter, B. S., Joshi, R., Karmarkar, N. K. "A Projective Geometry Architecture for Scientific Computation". Proceedings of International Conference on Application Specific Array Processors, IEEE Computer Society, p. 6480 (1992).
- ^ Karmarkar, N. K. "A New Parallel Architecture for Scientific Computation Based on Finite Projective Geometries". Proceeding of Mathematical Programming, State of the Art, p. 136148 (1994).
- ^ "Golden Plate Awardees of the American Academy of Achievement". www.achievement.org. American Academy of Achievement.
- ^ "Whiz kids rub elbows with right stuff" (PDF). Rocky Mountain News. 30 June 1985.
External links
edit- Distinguished Alumnus 1996 IIT Bombay
- Flashback: An Interior Point Method for Linear Programming IIT Bombay Heritage Fund
- Karmarkar function in Scilab