Computing shortest monotone paths on simple polytopes is NP-hard, implying NP-hardness for shortest simplex pivot sequences and polytope diameters, with a polynomial-time result via small simple extended formulations.
Sanità,The diameter of the fractional matching polytope and its hardness implications, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), 2018, pp
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Finding Short Paths on Simple Polytopes
Computing shortest monotone paths on simple polytopes is NP-hard, implying NP-hardness for shortest simplex pivot sequences and polytope diameters, with a polynomial-time result via small simple extended formulations.