Improvements in DNA sequencing have both broadened its utility and dramatically increased the size of sequencing datasets. Sequencing instruments are now used regularly as sources of high-resolution evidence for genotyping, methylation profiling, DNA-protein interaction mapping, and characterizing gene expression in the human genome and in other species. With existing methods, the computational cost of aligning short reads from the Illumina instrument to a mammalian genome can be very large: on the order of many CPU months for one human genotyping project. This thesis presents a novel application of the Burrows-Wheeler Transform that enables the alignment of short DNA sequences to mammalian genomes at a rate much faster than existing hashtable-based methods. The thesis also presents an extension of the technique that exploits the scalability of Cloud Computing to perform the equivalent of one human genotyping project in hours.