Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 06, 2006, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Robin Moser

How good is the information theory bound in sorting?

Given an ordering w ∈ ∪ A_j we want to determine to which subset A_j the ordering w belongs by performing a sequence of comparisons between the elements of S. The classical sorting problem corresponds to the case where the subsets A_j comprise the n! singleton sets of orderings.

If a sorting problem is defined by r nonempty subsets A_j, then the information theory bound states that at least log₂(r) comparisons are required to solve that problem in the worst case. The purpose of this paper is to investigate the accuracy of this bound. While we show that it is usually very weak, we are nevertheless able to define a large class of problems for which this bound is good. As an application, we show that if X and Y are n element sets of real numbers, then the n² element set X+Y can be sorted with O(n²) comparisons, improving upon the n²log(n) bound established by Harper et al. The problem of sorting X+Y was posed by Berlekamp."

[1] Fredman, M., How good is the information theory bound in sorting?, Theoretical Computer Science 1 (4), 1976, pp. 355-361.

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