On a constant arising in the analysis of bit comparisons in quickselect

Abstract

A (real) constant that appears as the factor of the leading term of the average number of bit comparisons required by quickselect, and was originally given in terms of complex numbers, is expressed using real numbers alone. A further representation is derived which is converging very quickly. Methods include residue calculus and the Euler-MacLaurin summation formula.

Keywords: Bit comparisons, quickselect, residues, Euler-MacLaurin formula

Quaestiones Mathematicae 31(2008), 303–306