The last two decades have seen an exponential increase in genomic and biomedical data, which will soon outstrip advances in computing power. Extracting new science from these massive datasets will require not only faster computers; it will require algorithms that scale sublinearly in the size of the datasets. We introduce a novel class of algorithms that are able to scale with the entropy and low fractal dimension of the dataset by taking advantage of the unique structure of massive biological data to operate directly on compressed data. These algorithms can be used to address large-scale challenges in genomics, metagenomics and chemogenomics.