Best laid plans of lions and men

Mikkel Abrahamsen, Jacob Holm, Eva Rotenberg, Christian Wulff-Nilsen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

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
Number of pages556
Volume77
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication date1 Jun 2017
Pages61-616
ISBN (Electronic)9783959770385
DOIs
Publication statusPublished - 1 Jun 2017
Event33rd International Symposium on Computational Geometry, SoCG 2017 - Brisbane, Australia
Duration: 4 Jul 20177 Jul 2017

Conference

Conference33rd International Symposium on Computational Geometry, SoCG 2017
CountryAustralia
CityBrisbane
Period04/07/201707/07/2017
SponsorUniversity of Queensland

Keywords

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

Cite this

Abrahamsen, M., Holm, J., Rotenberg, E., & Wulff-Nilsen, C. (2017). Best laid plans of lions and men. In 33rd International Symposium on Computational Geometry, SoCG 2017 (Vol. 77, pp. 61-616). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2017.6