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It will be of excellent sensible and theoretical importance to learn no matter whether any this kind of variants exist, especially as an method of determining if LP is often solved in strongly polynomial time.
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This is actually the initially worst-scenario polynomial-time algorithm at any time discovered for linear programming. To unravel an issue which has n variables and might be encoded in L input bits, this algorithm runs in O ( n 6 L ) displaystyle O(n^ six L)
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This intently linked list of troubles is cited by Stephen Smale as One of the eighteen biggest unsolved issues of your 21st century. In Smale's text, the 3rd Variation of the challenge "is the main unsolved difficulty of linear programming principle." While algorithms exist to solve linear programming in weakly polynomial time, see this page such as the ellipsoid techniques and inside-point tactics, no algorithms have but been observed that make it possible for strongly polynomial-time overall performance in the number of constraints and the amount of variables.