Lévy strategies in intermittent search processes are advantageous
- *MEMPHYS Center for Biomembrane Physics, Department of Physics and Chemistry, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark;
- †Physics Department, Technical University of Munich, James Franck Strasse, D-85747 Garching, Germany; and
- ‡School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
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Communicated by Joshua Jortner, Tel Aviv University, Tel Aviv, Israel, and approved April 6, 2008 (received for review January 8, 2008)
Abstract
Intermittent search processes switch between local Brownian search events and ballistic relocation phases. We demonstrate analytically and numerically in one dimension that when relocation times are Lévy distributed, resulting in a Lévy walk dynamics, the search process significantly outperforms the previously investigated case of exponentially distributed relocation times: The resulting Lévy walks reduce oversampling and thus further optimize the intermittent search strategy in the critical situation of rare targets. We also show that a searching agent that uses the Lévy strategy is much less sensitive to the target density, which would require considerably less adaptation by the searcher.
Footnotes
- §To whom correspondence should be addressed. E-mail: metz{at}ph.tum.de
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Author contributions: M.A.L., T.K., R.M., and J.K. designed research, performed research, analyzed data, and wrote the paper.
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The authors declare no conflict of interest.
- © 2008 by The National Academy of Sciences of the USA
