Some NP-complete problems in linear programming
Operations Research Letters
Parallel pipelined filter ordering with precedence constraints
ACM Transactions on Algorithms (TALG)
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Although it is NP-complete to decide whether a linear programming problem is degenerate, the @e-perturbation method can be used to reduce in polynomial time any linear programming problem with rational coefficients to a nondegenerate problem. The perturbed problem has the same status as the given one in terms of feasibility and unboundedness, and optimal bases of the perturbed problem are optimal in the given problem.