Lecture 15 : Sortedness , Connectivity , MST Weight , Components
نویسنده
چکیده
which consists of an increasing sequence of m decreasing sequences, each of length n/m. The longest increasing subsequence has length m but but the only way for the sample to imply that the input is not sorted is if two chosen elements land in the same decreasing sequence. The probability that this happens is at most ( s 2 ) /m ≤ s/(2m) which is o(1) if s is o( √ m). In particular, for ε = 1/2 and m = n/2, s = Ω( √ n) is required.
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