Parallel Searching on m Rays

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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(s) Hammar, Mikael ; Nilsson, Bengt J. ; Schuierer, Sven
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(s) Computational Geometry
Online Search Strategies
Research Subject Categories::MATHEMATICS::Applied mathematics::Theoretical computer science
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