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# Parallel Searching on m Rays

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 Publication Article, peer reviewed scientific Title Parallel Searching on m Rays Author ; ; Date 2001 English abstract We investigate parallel searching on $m$ concurrent rays. We assume that a target $t$ is located somewhere on one of the rays; we are given a group of $m$ point robots each of which has to reach $t$. Furthermore, we assume that the robots have no way of communicating over distance. Given a strategy $S$ we are interested in the competitive ratio defined as the ratio of the time needed by the robots to reach $t$ using $S$ and the time needed to reach $t$ if the location of $t$ is known in advance. If a lower bound on the distance to the target is known, then there is a simple strategy which achieves a competitive ratio of~9 --- independent of $m$. We show that 9 is a lower bound on the competitive ratio for two large classes of strategies if $m\geq 2$. If the minimum distance to the target is not known in advance, we show a lower bound on the competitive ratio of $1 + 2 (k + 1)^{k + 1} / k^k$ where $k = \left\lceil\log m\right\rceil$ where $\log$ is used to denote the base 2 logarithm. We also give a strategy that obtains this ratio. Publisher Elsevier Host/Issue Computational Geometry: Theory and Applications;3 Volume 18 Pages 125-139 Language eng (iso) Subject Computational GeometryOnline Search StrategiesSciencesResearch Subject Categories::MATHEMATICS::Applied mathematics::Theoretical computer science Handle http://hdl.handle.net/2043/6643 Permalink to this page
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