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Problem 8: Linear Programming: Strongly Polynomial?


Is linear programming strongly polynomial?


Nimrod Megiddo [Meg82][Meg83].



Partial and Related Results

It is known to be weakly polynomial, that is, polynomial in the bit complexity of the input data [Kha80], [Kar84]. Subexponential time is achievable via a randomized algorithm [MSW96]. In any fixed dimension, linear programming can be solved in strongly polynomial linear time (linear in the input size), established in dimensions 2 and 3 in [Dye84] and for all dimensions in [Meg84].




linear programming

Entry Revision History

J. O’Rourke, 2 Aug 2001, 16 Jul 2007; E. Demaine, 12 Mar 2010.



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