Approximating the Maximum Isomorphic Agreement Subtree Is Hard
The Maximum Isomorphic Agreement Subtree (MIT) problem is one of the simplest versions of the Maximum Interval Weight Agreement Subtree method (MIWT) which is used to compare phylogenies. More precisely MIT allows to provide a subset of the species such that the exact distances between species in such subset is preserved among all evolutionary trees considered. In this paper, the approximation complexity of the MIT problem is investigated, showing that it cannot be approximated in polynomial time within factor logδn for any δ > 0 unless NP ⊂ DTIME(2polylog n) for instances containing three trees. Moreover, we show that such result can be strengthened whenever instances of the MIT problem can contain an arbitrary number of trees, since MIT shares the same approximation lower bound of MAX CLIQUE.
Unable to display preview. Download preview PDF.
- 2.R. Cole, M. Farach, R. Hariharan, T. Przytycka, and M. Thorup. An O(n log n) algorithm for the maximum agreement subtree problem for binary trees. SIAM Journal on Computing, to appear.Google Scholar
- 3.R. Cole and R. Hariharan. An O(n log n) algorithm for the maximum agreement subtree problem for binary trees. In Proc. of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA96), pages 323–332, 1996.Google Scholar
- 8.J. Håstad. Clique is hard to approximate within n1-∈. Acta Mathematica, to appear.Google Scholar
- 9.J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. In Z. Galil and E. Ukkonen, editors, Proceedings of the 6th Annual Symposium on Combinatorial Pattern Matching (CPM95), volume 937 of LNCS, pages 177–190. Springer-Verlag, 1995.Google Scholar
- 11.V. Kann. On the approximability of the maximum common subgraph problem. In Proc. 9th Ann. Symp. on Theoretical Aspects of Comput. Sci. (STACS92), volume 577 of LNCS, pages 377–388, 1992.Google Scholar
- 12.M.-Y. Kao. Tree contractions and evolutionary trees. SIAM Journal on Computing, to appear.Google Scholar
- 13.M.-Y. Kao, T. W. Lam, T. M. Przytycka, W.-K. Sung, and H.-F. Ting. General techniques for comparing unrooted evolutionary trees. In Proceedings of the 29th Symposium on the Theory of Computing (STOC97), pages 54–65, 1997.Google Scholar
- 15.T. Lam, W. Sung, and H. Ting. Computing the unrooted maximum agreement subtree in subquadratic time. In Proc. of the 5th Scandinavian Workshop on ALgorithms Theory, LNCS, pages 124–135, 1996.Google Scholar