On extremal sort sequences

  • Authors:

  • Minyoung Yun;Young Wook Keum

  • Affiliations:

  • Division of Computer Engineering, Sungkyul University, Anyang 430-742, Korea;Division of Computer Engineering, Sungkyul University, Anyang 430-742, Korea

  • Venue:
  • The Korean Journal of Computational & Applied Mathematics
  • Year:
  • 2002

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Abstract

A sort sequence Sn is a sequence of all unordered pairs of indices in In = {1, 2, ..., n}. With a sort sequence Sn = (s1, s2, ..., s(n 2)), one can associate a predictive sorting algorithm A(Sn). An execution of the algorithm performs pairwise comparisons of elements in the input set X in the order defined by the sort sequence Sn except that the comparisons whose outcomes can be inferred from the results of the preceding comparisons are not performed. A sort sequence is said to be extremal if it maximizes a given objective function. First we consider the extremal sort sequences with respect to the objective function ω(Sn) - the expected number of active predictions in Sn. We study ω-extremal sort sequences in terms of their prediction vectors. Then we consider the objective function Ω(Sn) - the minimum number of active predictions in Sn over all input orderings.