[2] He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method.
During this time, he was funded by Ratan Tata to scale-up the supercomputer he had designed and prototyped at TIFR.
He was the founding director of Computational Research labs in Pune, where the scaling-up work was performed.
Karmarkar's algorithm solves linear programming problems in polynomial time.
Karmarkar's algorithm has stimulated the development of several interior-point methods, some of which are used in current implementations of linear-program solvers.