Michael Hoffmann

  1. Counting Plane Graphs: Flippability and its Applications.

    Authors: Micha Sharir, Csaba D. Tóth, Adam Sheffer, Emo Welzl, Michael Hoffmann
    Subjects: Discrete Mathematics
    Abstract

    We generalize the notions of flippable and simultaneously-flippable edges in
    a triangulation of a set S of points in the plane, into so called pseudo
    simultaneously-flippable edges. Such edges are related to the notion of convex
    decompositions spanned by S.

  2. Minimum and maximum against k lies.

    Authors: Jiří Matoušek, Yoshio Okamoto, Michael Hoffmann, Philipp Zumstein
    Subjects: Data Structures and Algorithms
    Abstract

    A neat 1972 result of Pohl asserts that [3n/2]-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 Renyi-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.

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