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 -