Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, February 23, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Michael Hoffmann

Min and Max with k Lies

A neat 1972 result of Pohl asserts that \lceil 3n/2 \rceil -2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Rényi--Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+\O(\sqrt{k}))n comparisons suffice.

We improve on this by providing an algorithm with at most (k+1+C)n+\O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32= 0.71875, and c_k=\Omega(2^{-5k/4}) as k\to\infty.

Joint work with Jirka Matousek, Yoshio Okamoto, and Philipp Zumstein

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