Computational complexity of inferring phylogenies from chromosome inversion data.

In systematics, parsimony methods construct phylogenies, or evolutionary trees, in which characters evolve with the least evolutionary change. The chromosome inversion, or polymorphism, parsimony criterion is used when each character of a population may exhibit homozygous or heterozygous states, but when the heterozygous state must evolve uniquely. Variations of the criterion concern whether or not the ancestral states of characters are specified. We establish that problems of inferring phylogenies by these criteria are NP-complete and thus are so difficult computationally that efficient optimal algorithms for them are unlikely to exist.