description Narendra Karmarkar Overview
Narendra Karmarkar is an Indian mathematician and computer scientist who, in 1984 while at Bell Laboratories, published a polynomial-time interior-point algorithm for linear programming. The algorithm offered competitive practical performance against the simplex method for large-scale optimization problems and sparked renewed interest in interior-point methods. His work has been recognized as a major milestone in mathematical optimization. He later pursued research in information theory and polynomial complexity methods.
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Narendra Karmarkar ranks #92 of 185 in the Computer Scientist ranking, behind Ran Raz, ahead of Philip Wadler.
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What is Karmarkar's algorithm and why was it significant?
Karmarkar's algorithm, introduced in 1984, was a polynomial-time interior-point method for linear programming that demonstrated practical performance competitive with or superior to the simplex method on large problems. It caused a sensation in the optimization community because it proved interior-point methods could be both theoretically efficient and practically useful.
How does Karmarkar's algorithm differ from the simplex method?
The simplex method moves along the edges of the feasible polytope and has exponential worst-case complexity, while Karmarkar's interior-point method traverses the interior of the polytope using projective transformations. Karmarkar's approach achieves polynomial-time complexity and can outperform the simplex method on very large instances.
Where was Narendra Karmarkar working when he published his algorithm?
Karmarkar developed his algorithm while working at Bell Laboratories (Bell Labs). His 1984 presentation at the ACM Symposium on Theory of Computing (STOC) generated enormous excitement in both the theoretical and applied optimization communities.
What was the practical and commercial impact of Karmarkar's algorithm?
Karmarkar's algorithm had immediate practical impact on industries that rely on large-scale linear programming, including telecommunications network optimization, transportation logistics, and manufacturing planning. AT&T, which owned Bell Labs, pursued patents on the algorithm and incorporated it into its commercial optimization software.
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