  Forthcoming high-resolution observations of the Cosmic Microwave Background
(CMB) radiation will generate datasets many orders of magnitude larger than
have been obtained to date. The size and complexity of such datasets presents a
very serious challenge to analysing them with existing or anticipated
computers. Here we present an investigation of the currently favored algorithm
for obtaining the power spectrum from a sky-temperature map --- the quadratic
estimator. We show that, whilst improving on direct evaluation of the
likelihood function, current implementations still inherently scale as the
equivalent of the cube of the number of pixels or worse, and demonstrate the
critical importance of choosing the right implementation for a particular
dataset.
