The exploration and interpretation of large, complex datasets is vital to discovery in genomics. However, researchers now confront a fundamental limitation; unprecedented experiments are possible thanks to modern DNA sequencing technologies, yet existing genome arithmetic techniques for comparing and dissecting the resulting datasets are incapable of keeping pace with inexorable growth in dataset size and complexity. Genome arithmetic (GA) represents a powerful and widely used set of techniques that allow one to explore relationships among sets of genome features (e.g., a gene, sequence alignment, ChIP-seq peak, or anything that can be described with chromosome coordinates). GA is used for a broad spectrum of analyses including: the detection of intersecting/overlapping features (e.g., sequence alignments and exons), describing feature coverage among datasets, and the merging, subtraction, and complementation of feature datasets. GA functionality is used by all genome browsers and data visualization tools, and by analysis software such as GATK and SAMTOOLS. Owing to their power and flexibility, existing GA tools (i.e., Galaxy, the UCSC Genome Browser, and our own BEDTOOLS) are extremely popular and are used in a broad range of complex genomic analyses. However, while GA is central to genomic analysis and discovery, the core algorithms employed by all existing tools are inherently incapable of scaling to the scale and diversity of modern genomic datasets. Restricted to these approaches, the present analytic bottleneck will become increasingly acute. Therefore, the overall objective of this proposal is to provide the genomics community with innovative new algorithms and software that keep pace with modern genomics experiments and facilitate future discoveries. The Specific Aims are to: (1) Devise efficient new algorithms for large-scale genome arithmetic analyses. We will develop innovative GA algorithms that scale to modern genomics experiments and are capable of integrating many diverse genomic datasets. We will devise novel algorithms and adapt proven, scalable approaches from the field of computational geometry. (2) Develop software and libraries that facilitate innovative analyses and new tool development. We will release our algorithms to the community as open-source software libraries and tools that will foster new tool development and provide innovative approaches for exploring large-scale datasets. (3) Extend our tools to scalable computing frameworks in order to enable future genomic discovery. We will adapt our software to parallel computing environments and thereby enable continued discovery on increasingly massive and complex datasets. The proposed research will devise entirely new, scalable approaches for genome arithmetic. This will provide the community with powerful new techniques for exploring and interpreting genomics experiments and provide tool developers with robust approaches for software development and improvement.