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LIPIcs - Leibniz International Proceedings in Informatics. 25th International Symposium on Theoretical Aspects of Computer Science
Doi
Abstract
We analyze a simple random process in which a token is moved in the
interval A={0,dots,n: Fix a probability distribution mu
over {1,dots,n. Initially, the token is placed in a random
position in A. In round t, a random value d is chosen
according to mu. If the token is in position ageqd, 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 mu. More precisely, we show that
min_mu{E_mu(T)=Thetaleft((log n)^2
ight). 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\u27\u27 optimization
strategy
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