Ann-dimensional search problem with restricted questions

Abstract

The problem is the following: How many questions are necessary in the worst case to determine whether a pointX in then-dimensional Euclidean spaceR n belongs to then-dimensional unit cubeQ n, where we are allowed to ask which halfspaces of (n−1)-dimensional hyperplanes contain the pointX? It is known that ⌌3n/2⌍ questions are sufficient. We prove here thatcn questions are necessary, wherec≈1.2938 is the solution of the equationx log2 x−(x−1) log2 (x−1)=1.

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References

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Győri, E. Ann-dimensional search problem with restricted questions. Combinatorica 1, 377–380 (1981). https://doi.org/10.1007/BF02579459

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AMS subject classification (1980)

  • 05 A 05
  • 05 A 99