Rapid advances in next-generation sequencing technologies are revolutionizing genomics, with data sets at the scale of thousands of human genomes fast becoming the norm. These technological leaps promise to enable corresponding advances in biology and medicine, but the deluge of raw data poses substantial mathematical, computational and statistical challenges that must first be overcome. This thesis consists of two research thrusts along these lines. First, we propose an algorithmic framework, "compressive genomics," that accelerates bioinformatic computations through analysis-aware compression. We demonstrate this methodology with proof-of-concept implementations of compression-accelerated search (CaBLAST and CaBLAT). Second, we develop new computational tools for investigating population admixture, a phenomenon of importance in understanding demographic histories of human populations and facilitating association mapping of disease genes. Our recently released ALDER and MixMapper software packages provide fast, sensitive, and robust methods for detecting and analyzing signatures of admixture created by genetic drift and recombination on genome-wide, large-sample scales.
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