The co phylogeny reconstruction problem is NP-complete.

The co phylogeny reconstruction problem is that of finding minimum cost explanations of differences between historical associations. The problem arises in parasitology, molecular systematics, and biogeography. Existing software tools for this problem either have worst-case exponential time or use heuristics that do not guarantee optimal solutions. To date, no polynomial time optimal algorithms have been found for this problem. In this article, we prove that the problem is NP-complete, suggesting that future research on algorithms for this problem should seek better polynomial-time approximation algorithms and heuristics rather than optimal solutions.