Comparing DNA or protein sequences plays an important role in the functional analysis of
genomes. Despite many methods available for sequences comparison, few methods retain
the information content of sequences. We propose a new approach, the Yau-Hausdorff
method, which considers all translations and rotations when seeking the best match of
graphical curves of DNA or protein sequences. The complexity of this method is lower than
that of any other two dimensional minimum Hausdorff algorithm. The Yau-Hausdorff method
can be used for measuring the similarity of DNA sequences based on two important tools:
the Yau-Hausdorff distance and graphical representation of DNA sequences. The graphical
representations of DNA sequences conserve all sequence information and the Yau-Hausdorff
distance is mathematically proved as a true metric. Therefore, the proposed distance
can preciously measure the similarity of DNA sequences. The phylogenetic analyses of
DNA sequences by the Yau-Hausdorff distance show the accuracy and stability of our
approach in similarity comparison of DNA or protein sequences. This study demonstrates
that Yau-Hausdorff distance is a natural metric for DNA and protein sequences with high
level of stability. The approach can be also applied to similarity analysis of protein
sequences by graphic representations, as well as general two dimensional shape
matching.