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Revisiting the Problem of Searching on a Line

  • Prosenjit Bose
  • Jean-Lou De Carufel
  • Stephane Durocher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

Abstract

We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the first tight bounds on the exact optimal competitive ratio achievable, parametrized in terms of the given range for D, along with an optimal search strategy that achieves this competitive ratio. We prove that this optimal strategy is unique and that it cannot be computed exactly in general. We characterize the conditions under which an optimal strategy can be computed exactly and, when it cannot, we explain how numerical methods can be used efficiently. In addition, we answer several related open questions and we discuss how to generalize these results to m rays, for any m ≥ 2.

Keywords

Search Strategy Optimal Strategy Polynomial Equation Competitive Ratio Galois Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Jean-Lou De Carufel
    • 1
  • Stephane Durocher
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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