High-throughput sequencing techniques have initiated a new era in biomedical sciences: In cancer research, it is now feasible to analyse evolution of mutations based on sequencing data and tailor treatment based on such analysis. Evolution of species can be explored by sequencing thousands of individuals. Research area of Algorithmic Bioinformatics aims to provide a solid foundation for reliable and scalable methods to enable new breakthroughs based on high-throughput sequencing data. The methods and theoretical foundations we develop span several algorithm engineering and theoretical computer science branches such as string algorithms, data compression, and graph algorithms. While our motivation comes from sequencing related analysis tasks, we aim for solid advances that may have applications beyond the specific problem at hand.