TY - GEN
T1 - On the complexity of computing evolutionary trees
AU - Gasieniec, Leszek
AU - Jansson, Jesper Andreas
AU - Lingas, Andrzej
AU - Östlin, Anna
PY - 1997/1/1
Y1 - 1997/1/1
N2 - In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part, of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of Nε, where N is the input size, for any 0 ≤ ε < 1/18 in polynomial time unless P=NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and we provide a simple fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.
AB - In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part, of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of Nε, where N is the input size, for any 0 ≤ ε < 1/18 in polynomial time unless P=NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and we provide a simple fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.
UR - http://www.scopus.com/inward/record.url?scp=84877796796&partnerID=8YFLogxK
M3 - Conference article published in proceeding or book
SN - 354063357X
SN - 9783540633570
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 134
EP - 145
BT - Computing and Combinatorics - 3rd Annual International Conference COCOON 1997, Proceedings
PB - Springer Verlag
T2 - 3rd Annual International Computing and Combinatorics Conference, COCOON 1997
Y2 - 20 August 1997 through 22 August 1997
ER -