Tight Bounds for Blind Search on the Integers
| dc.creator | Dietzfelbinger, Martin | |
| dc.creator | Rowe, Jonathan E. | |
| dc.creator | Wegener, Ingo | |
| dc.creator | Woelfel, Philipp | |
| dc.date | 2008-02-20 | |
| dc.date.accessioned | 2026-07-07T09:22:03Z | |
| dc.date.available | 2026-07-07T09:22:03Z | |
| dc.description | 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 $a\geq d$, 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 $μ$. More precisely, we show that $\min_μ\{E_μ(T)\=Θ((\log n)^2)$. 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. | |
| dc.identifier | https://arxiv.org/abs/0802.2852 | |
| dc.identifier | http://arxiv.org/abs/0802.2852 | |
| dc.identifier | Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155239 | |
| dc.subject | Data Structures and Algorithms | |
| dc.title | Tight Bounds for Blind Search on the Integers | |
| dc.type | text |