Optimal algorithms for 2 × n AB games - A graph-partition approach

Shan Tai Chen, Shun-Shii Lin

研究成果: 雜誌貢獻期刊論文同行評審

9 引文 斯高帕斯(Scopus)

摘要

This paper presents new and systematic methodologies to analyze deductive games and obtain optimal algorithms for 2 × n AB games, where n ≥ 2. We have invented a graphic model to represent the game-guessing process. With this novel approach, we find some symmetric and recursive structures in the process. This not only reduces the size of the search space, but also helps us to derive the optimum strategies more efficiently. By using this technique, we develop optimal strategies for 2 × n AB games in the expected and worst cases, and are able to derive the following new results: (1) ⌈n/2⌉ + 1 guesses are necessary and sufficient for 2 × n AB games in the worst case, (2) the minimum number of guesses required for 2 × n AB games in the expected case is (4n3 + 21n2-76n + 72)/12n(n - 1) if n is even, and (4n3 + 21n2 - 82n + 105)/12n(n - 1) if n is odd. The optimization of this problem bears resemblance with other computational problems, such as circuit testing, differential cryptanalysis, on-line models with equivalent queries, and additive search problems. Any conclusion of this kind of deductive game may be applied, although probably not directly, to any of these problems, as well as to any other combinatorial optimization problem.

原文英語
頁(從 - 到)105-126
頁數22
期刊Journal of Information Science and Engineering
20
發行號1
出版狀態已發佈 - 2004 一月 1

ASJC Scopus subject areas

  • 軟體
  • 人機介面
  • 硬體和架構
  • 圖書館與資訊科學
  • 計算機理論與數學

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