Hunting for Functionally Analogous Genes

Evidence indicates that members of many gene families in the genome of an organism tend to have homologues both within their own genome and in the genomes of other organisms. Amongst these homologues, typically only one or a few per genome perform an analogous function in their genome. Finding subsets of these genes which show evidence of performing a common function is an important rst step towards, for instance, the creation of phylogenetic trees, multiple sequence alignments and secondary structure predictions. ask to choose one gene from each of the taxa Pi such that these chosen vertices most agree. We deene most agreeing in four distinct ways: most tree-like, pairwise closest, pairwise most similar, and smallest most tree-like. We show these problems to be computationally hard from almost every angle via classical, param-eterized and approximation complexity theory. However, on the positive side, we give randomized approximation algorithms following ideas from GGR98] for the pairwise closest and pairwise most similar variants.