Best laid plans of lions and men

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We answer the following question dating back to J. E. Littlewood (1885-1977): Can two lions catch a man in a bounded area with rectifiable lakes? The lions and the man are all assumed to be points moving with at most unit speed. That the lakes are rectifiable means that their boundaries are finitely long. This requirement is to avoid pathological examples where the man survives forever because any path to the lions is infinitely long. We show that the answer to the question is not always "yes" by giving an example of a region R in the plane where the man has a strategy to survive forever. R is a polygonal region with holes and the exterior and interior boundaries are pairwise disjoint, simple polygons. Our construction is the first truly two-dimensional example where the man can survive. Next, we consider the following game played on the entire plane instead of a bounded area: There is any finite number of unit speed lions and one fast man who can run with speed 1 + ϵ for some value ϵ > 0. Can the man always survive? We answer the question in the affirmative for any constant ϵ > 0.

Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry (SoCG 2017)
EditorsBoris Aronov, Matthew J. Katz
Number of pages16
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication date2017
Article number6
ISBN (Electronic)978-3-95977-038-5
Publication statusPublished - 2017
Event33rd International Symposium on Computational Geometry - Brisbane, Australia
Duration: 4 Jul 20177 Jul 2017
Conference number: 33


Conference33rd International Symposium on Computational Geometry
SeriesLeibniz International Proceedings in Informatics

    Research areas

  • Lion and man game, Pursuit evasion game, Winning strategy

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