Patent Controversy
At the time he invented the algorithm, Narendra Karmarkar was employed by AT&T and they realized that his invention could be of practical importance. In April 1985, AT&T promptly applied for a patent on Karmarkar's algorithm and that became more fuel for the ongoing controversy over the issue of software patents. This left many mathematicians uneasy, such as Ronald Rivest (himself one of the holders of the patent on the RSA algorithm), who expressed the opinion that research proceeded on the basis that algorithms should be free. Even before the patent was actually granted, it seemed that there was prior art that might have been applicable. Mathematicians who specialize in numerical analysis such as Philip Gill and others showed that Karmarkar's algorithm is actually equivalent to a projected Newton barrier method with a logarithmic barrier function, if the parameters are chosen suitably. Methods referred to by Gill were widely used for nonlinear programming since the 1960s. In fact, one well-known book first published in 1968 described the technique specifically in the context of linear programming. However, some say Gill's argument is flawed, insofar as the method they describe does not even qualify as an "algorithm", since it requires choices of parameters that don't follow from the internal logic of the method, but rely on external guidance, essentially from Karmarkar's algorithm. Furthermore, Karmarkar's contributions are considered far from obvious in light of all prior work, including Fiacco-McCormick, Gill and others cited by Saltzman. The patent was eventually granted as U.S. Patent 4,744,026: "Methods and apparatus for efficient resource allocation" in May 1988. The patent, however, proved to be of limited commercial value to AT&T. They built up the KORBX system, an 8-processor Alliant computer incorporating linear programming software using Karmarkar's algorithm, priced at US$8.9 million each, and they only managed to sell two such systems. Opponents of software patents have further alleged that the patents ruined the positive interaction cycles that previously characterized the relationship between researchers in linear programming and industry, and specifically it isolated Karmarkar himself from the network of mathematical researchers in his field.
The patent itself expired in April 2006, and the algorithm is presently in the public domain.
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