针对k个谎言的最小值和最大值
Minimum and maximum against k lies
摘要：
Pohl在1972年的一个简洁的结果断言，[3 n/2]-2次比较是足够的，并且在最坏的情况下也是必要的，可以找到一个n元全序集的最小值和最大值。通过oracle访问该集合以进行成对比较。最近，这个问题已经在Renyi-Ulam说谎者游戏的背景下进行了研究，其中预言机可能会给出k个错误的答案。对于大的k，由于Aigner的上界表明（k+O（\sqrt{k}））n次比较就足够了。我们对此进行了改进，提供了一个算法，对于某个常数C，最多有（k+1+C）n+O（k^3）次比较。已知的下界为（k+1+c_k）n-D，其中c_0=0.5，c_1=23/32=0.71875，当k趋于无穷大时，c_k=Ω（2^{-5k/4}）。
英文摘要：
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. 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=Ω(2^{-5k/4}) as k goes to infinity.
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