Competitive Searching for a Line on a Line Arrangement

Authors Quirijn Bouts, Thom Castermans, Arthur van Goethem, Marc van Kreveld, Wouter Meulemans

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Quirijn Bouts
  • ASML Veldhoven, the Netherlands
Thom Castermans
  • TU Eindhoven, the Netherlands
Arthur van Goethem
  • TU Eindhoven, the Netherlands
Marc van Kreveld
  • Utrecht University, the Netherlands
Wouter Meulemans
  • TU Eindhoven, the Netherlands

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Quirijn Bouts, Thom Castermans, Arthur van Goethem, Marc van Kreveld, and Wouter Meulemans. Competitive Searching for a Line on a Line Arrangement. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 49:1-49:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We discuss the problem of searching for an unknown line on a known or unknown line arrangement by a searcher S, and show that a search strategy exists that finds the line competitively, that is, with detour factor at most a constant when compared to the situation where S has all knowledge. In the case where S knows all lines but not which one is sought, the strategy is 79-competitive. We also show that it may be necessary to travel on Omega(n) lines to realize a constant competitive ratio. In the case where initially, S does not know any line, but learns about the ones it encounters during the search, we give a 414.2-competitive search strategy.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Competitive searching
  • line arrangement
  • detour factor
  • search strategy


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