# The Simplex Algorithm Is NP-Mighty

@article{Disser2019TheSA, title={The Simplex Algorithm Is NP-Mighty}, author={Y. Disser and M. Skutella}, journal={ACM Transactions on Algorithms (TALG)}, year={2019}, volume={15}, pages={1 - 19} }

We show that the Simplex Method, the Network Simplex Method—both with Dantzig’s original pivot rule—and the Successive Shortest Path Algorithm are NP-mighty. That is, each of these algorithms can be used to solve, with polynomial overhead, any problem in NP implicitly during the algorithm’s execution. This result casts a more favorable light on these algorithms’ exponential worst-case running times. Furthermore, as a consequence of our approach, we obtain several novel hardness results. For… Expand

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