OPTIMAL SETS OF QUESTIONS FOR TWENTY QUESTIONS

Yuval Filmus, Idan Mehalel

Research output: Contribution to journalArticlepeer-review

Abstract

In the distributional Twenty Questions game, Bob chooses a number x from 1 to n according to a distribution μ, and Alice (who knows μ) attempts to identify x using yes/no questions, which Bob answers truthfully. Her goal is to minimize the expected number of questions. The optimal strategy for the Twenty Questions game corresponds to a Huffman code for μ, yet this strategy could potentially uses all 2n possible questions. Dagan et al. constructed a set of 1.25n+o(n) questions which suffice to construct an optimal strategy for all μ, and showed that this number is optimal (up to subexponential factors) for infinitely many n. We determine the optimal size of such a set of questions for all n (up to subexponential factors), answering an open question of Dagan et al. In addition, we generalize the results of Dagan et al. to the d-ary setting, obtaining similar results with 1.25

Original languageEnglish
Pages (from-to)412-452
Number of pages41
JournalSIAM Journal on Discrete Mathematics
Volume38
Issue number1
DOIs
StatePublished - 2024

Keywords

  • combinatorial search
  • games
  • information theory

All Science Journal Classification (ASJC) codes

  • General Mathematics

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