Minimum average-case queries of q+1-ary search game with small sets

  • Authors:

  • Kun Meng;Chuang Lin;Wen An Liu;Yang Yang;Gyula O. H. Katona

  • Affiliations:

  • School of Computer and Communication Engineering, University of science and technology Beijing, Beijing, China and Department of Computer Science and Technology, Tsinghua University, Beijing, Chin ...;Department of Computer Science and Technology, Tsinghua University, Beijing, China;College of Mathematics and Information Science, Henan Normal University, Xinxiang, China;School of Computer and Communication Engineering, University of science and technology Beijing, Beijing, China;Rényi Institute Budapest, Hungary

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2012

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Abstract

Given a search space S={1,2,...,n}, an unknown element x^*@?S and fixed integers @?=1 and q=1, a q+1-ary @?-restricted query is of the following form: which one of the set {A"0,A"1,...,A"q} is the x^* in?, where (A"0,A"1,...,A"q) is a partition of S and |A"i|@?@? for i=1,2,...,q. The problem of finding x^* from S with q+1-ary size-restricted queries is called as a q+1-ary search game with small sets. In this paper, we consider sequential algorithms for the above problem, and establish the minimum number of average-case sequential queries when x^* satisfies the uniform distribution on S.