The analysis of the molecular structure called DNA is of particular interest for the understanding of the basic processes governing life. Correlation techniques implemented on digital computers are currently used to do this analysis, but the process is so slow that the mapping and sequencing of the entire human genome requires a computational breakthrough. This paper presents a new method of performing the analysis of DNA sequences with an optical time-integrating correlator. The method is characterized by short processing times that make the analysis of the entire human genome a tractable enterprise. A processing strategy and the resultant processing times are presented. Experimental proofs of concept for the two types of analysis specified by the strategy are also included.