Authors: Dietzfelbinger, Martin
Rowe, Jonathan E.
Wegener, Ingo
Woelfel, Philipp
Title: Tight bounds for blind search on the integers
Language (ISO): en
Abstract: We analyze a simple random process in which a token is moved in the interval A = [0,n]: Fix a probability distribution µ over [1,n]. Initially, the token is placed in a random position in A. In round t, a random value d is chosen according to µ. If the token is in position a >= d, then it is moved to position a-d. Otherwise it stays put. Let T be the number of rounds until the token reaches position 0. We show tight bounds for the expectation of T for the optimal distribution µ, i.e., we show that min_µ{E_µ(T)} = Theta((log n)^2). For the proof, a novel potential function argument is introduced. The research is motivated by the problem of approximating the minimum of a continuous function over [0,1] with a "blind" optimization strategy.
Subject Headings: computational complexity
evolutionary algorithms
lower bounds
Issue Date: 2008-01
Appears in Collections:Sonderforschungsbereich (SFB) 531

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