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How to Play Hot and Cold on a Line

  • Herman Haverkort
  • David Kübel
  • Elmar Langetepe
  • Barbara Schwarzwald
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

Abstract

Suppose we are searching for a target point t in the unit interval. To pinpoint the location of t, we issue query points \(q_1, \ldots , q_n \in [0,1]\). As a response, we obtain an ordering of the query points by distance to t. This restricts possible locations of t to a subinterval. We define the accuracy of a query strategy as the reciprocal of the size of the subinterval to which we can pinpoint t in the worst case. We describe a strategy with accuracy \(\Theta (n^2)\), which is at most a factor two from optimal if all query points are generated at once. With query points generated one by one depending on the response received on previous query points, we achieve accuracy \(\Omega (2.29^n)\), and prove that no strategy can achieve \(\Omega (3.66^n)\).

Keywords

Search games Combinatorial optimization Target localization Online/offline strategies 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Herman Haverkort
    • 1
  • David Kübel
    • 2
  • Elmar Langetepe
    • 2
  • Barbara Schwarzwald
    • 2
  1. 1.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands
  2. 2.Department of Computer ScienceUniversity of BonnBonnGermany

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