Narendra Karmarkar

Narendra K. Karmarkar (born 1957) is an Indian mathematician, renowned for developing Karmarkar's algorithm. He is listed as an ISI highly cited researcher.^[1]

Biography

Narendra Karmarkar was born in Gwalior to a Marathi family. Karmarkar received his B.Tech in Electrical Engineering from IIT Mumbai in 1978, M.S. from the California Institute of Technology and Ph.D. in Computer Science from the University of California, Berkeley.

He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey. Karmarkar was a professor at the Tata Institute of Fundamental Research in Mumbai.

He is currently working on a new architecture for supercomputing. Some of the ideas are published at ^[2] Fab5 conference organised by MIT center for bits and atoms. ^[3]

Karmarkar received a number of awards for his algorithm, among them:

• Paris Kanellakis Award, 2000 given by The Association for Computing Machinery.
• Distinguished Alumnus Award, Computer Science and Engineering, University of California, Berkeley (1993)
• Ramanujan Prize for Computing, given by Asian Institute Informatics (1989)
• Fulkerson Prize in Discrete Mathematics given jointly by the American Mathematical Society & Mathematical Programming Society (1988)
• Fellow of Bell Laboratories (1987- )
• Texas Instruments Founders’ Prize (1986)
• Marconi International Young Scientist Award (1985)
• Frederick W. Lanchester Prize of the Operations Research Society of America for the Best Published Contributions to Operations Research (1984)
• National Science Talent Award in Mathematics, India (1972, India)

Work

Karmarkar's algorithm

Main article: Karmarkar's algorithm

Karmarkar's algorithm solves linear programming problems in polynomial time. These problems are represented by "n" variables and "m" constraints. The previous method of solving these problems consisted of problem representation by an "x" sided solid with "y" 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 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 other interior point methods, some of which are used in current codes for solving linear programs.

Paris Kanellakis Award

The Association for Computing Machinery awarded him the prestigious Paris Kanellakis Award in 2000 for his work. The award citation reads:

For his theoretical work in devising an Interior Point method for linear programming that provably runs in polynomial time, and for his implementation work suggesting that Interior Point methods could be effective for linear programming in practice as well as theory. Together, these contributions inspired a renaissance in the theory and practice of linear programming, leading to orders of magnitude improvement in the effectiveness of widely-used commercial optimization codes.

Research on computer architecture

See also: Computer architecture and supercomputing

Galois geometry

See also: Finite geometry, Galois geometry, Finite fields, Linear code, and Projective geometry

After 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.^[4]

Current investigations

Currently, he is synthesizing these concepts with some new ideas he calls sculpturing free space (a non-linear analogue of what has popularly been described as folding the perfect corner).^[5] This approach allows him to extend this work to the physical design of machines. He is now publishing updates on his recent work,^[6] including an extended abstract.^[7] This new paradigm was presented at IVNC, Poland on 16 July 2008,^[8] and at MIT on 25 July 2008.^[9] Some of the recent work is published at ^[2] and Fab5 conference organised by MIT center for bits and atoms

References

1. ^ Thomson ISI. "Karmarkar, Narendra K., ISI Highly Cited Researchers". http://hcr3.isiknowledge.com/author.cgi?&link1=Browse&link2=Results&id=3416. Retrieved 2009-06-20. 
2. ^ ^{a b} http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5166089&isYear=2009
3. ^ http://cba.mit.edu/events/09.08.FAB5/
4. ^ Karmarkar, Narendra. "A new parallel architecture for sparse matrix computation based on finite projective geometries". Proceedings of the 1991 ACM/IEEE conference on Supercomputing. http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=126029. 
5. ^ Angier, Natalie (1984-12-03). "Folding the Perfect Corner". Time Magazine. http://www.time.com/time/magazine/article/0,9171,923774,00.html. Retrieved 2008-07-12. 
6. ^ Karmarmar, Narendra (2008-07-11). "Narendra Karmarkar's recent research". punetech.com. http://punetech.com/narendra-karmarkar. Retrieved 2008-07-12. 
7. ^ Karmarmar, Narendra (2008-07-11). "Massively Parallel Systems and Global Optimization" (PDF). punetech.com Narendra Karmarkar's recent work. http://punetech.com/narendra-karmarkar/extended_abstract.pdf. Retrieved 2008-07-12. 
8. ^ Karmarmar, Narendra (2008-07-14). "Vacuum nanoelectronics devices from the perspective of optimization theory" (PDF). punetech.com Narendra Karmarkar's recent work. http://punetech.com/narendra-karmarkar/OptimizationForIVNC08.pdf. Retrieved 2008-07-14. 
9. ^ Karmarkar, Narendra. "Seminar on Massively Parallel Systems and Global Optimization". Computation Research in Boston. http://www-math.mit.edu/crib/08/jul25.html. Retrieved 2008-07-12. 

External links

• Distinguished Alumnus 1996 IIT Bombay.
• Article with links IIT Bombay Heritage Fund.

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Name	Karmarkar, Narendra
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Date of birth	1957
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