Settling the Intractability of Multiple Alignment

摘要

In this paper some of the most fundamental problems in computational biology are proved intractable. The following problems are shown NP-hard for all binary or larger alphabets under all fixed metrics: multiple alignment with SP-score, star alignment, and tree alignment (for a given phytogeny). Earlier these problems have only been shown intractable for sporadic alphabets and distances, here the intractability is settled. Moreover, the construction can be extended to prove NP-hardness results for consensus patterns and substring parsimony.