Problems of computing the reversal distance between genomes are discussed. Problems of computing the reversal distance between genomes are fundamental problems of Computational Biology, these problems have important meanings in studying the biological race evolution and the bio-pharmaceuticals etc. The problem of evolutionary trees based on reversal distance between genomes and it's NPC property are especially discussed.
The paper briefly reviews NP-hard optimization problems and their inapproximability. The hardness of solving CLIQUE problem is specifically dis- cussed. A dynamic-programming algorithm and its improved version for CLIQUE are reviewed and some additional analysis is presented. The analysis implies that the improved algorithm, HEWN (hierarchical edge-weighted network), only provides a heuristic or useful method, but cannot be called a polynomial algorithm.
