We will start from a discussion of the algorithmic aspects of production, analysis, and storage for short-reads sequencing-data in a genomic research project. Along this path we will see what are the most established currently used computational tools, with some emphasis on some aspect in which we believe a deeper interaction between Computer Science and Biology would be most welcome. With this in mind, we will conclude with the description of an ongoing study on some intriguing combinatorial and computational problem suggested by the task of clustering data during (cancer-cell sub-population) analysis and classification. Some temporal aspect of this problem will be taken into account.