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RANDOM EDGE can be exponential on abstract cubes
2006
Advances in Mathematics
We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective
doi:10.1016/j.aim.2005.05.021
fatcat:mmftd7pxdrbmhc52h7h73ondeu