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

__Mittagsseminar Talk Information__ | |

**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 *log*_{2}(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 *n*^{2} element set
*X+Y* can be sorted with *O(n*^{2}) comparisons, improving upon the
*n*^{2}log(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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