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As biomolecular sequence data continue to be amassed at unprecedented rates, the design of effective computational methods and capabilities that can derive biologically significant information from them has become both increasingly challenging and imperative. In this tutorial, the audience will be first introduced to the different types of biomolecular sequence data and the wealth of information they encode. Following this technical grounding, high-performance computing approaches developed to address some of the most computationally challenging problems in genomics will be described. The contents will be presented in three parts: (i) In the first part, we will describe methods that were designed to query a sequence against a large sequence database. Two popular parallel approaches, mpiBLAST and ScalaBLAST, implementing the NCBI BLAST suite of programs will be described. (ii) Next, we will describe PaCE, which is a parallel DNA sequence clustering algorithm. As direct applications, we will discuss the clustering of large-scale Expressed Sequence Tag data and the assembly of complex genomes. (iii) Finally, we describe GRAPPA, which is a high-performance software suite developed for phylogenetic reconstruction of a collection of genomes or genes. Throughout the tutorial, emphasis will be on both scalability and effectiveness in exploiting large-scale state-of-the-art supercomputing technologies. The intended audience are academic and industry researchers, educators, and/or commercial application developers, with a computational background. No background in biology is assumed.