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Subexponential lower bounds for randomized pivoting rules for the simplex algorithm

Thomas Dueholm Hansen
(Aarhus University)
Onsdag, 9 marts, 2011, at 10:15-11:15, INCUBA Science Park, Room 112
The simplex algorithm is among the most widely used algorithms for solving linear programs in practice. Most deterministic pivoting rules are known, however, to need an exponential number of steps to solve some linear programs (Klee-Minty examples). No non-polynomial lower bounds on the expected number of steps were known, prior to this work, for randomized pivoting rules. We provide the first subexponential (i.e., of the form 2^(Omega(n^alpha)), for some alpha>0) lower bounds for the two most natural, and most studied, randomized pivoting rules suggested to date, thereby solving a problem open since the early 1970s.

Joint work with Oliver Friedmann and Uri Zwick, to appear at STOC'11.