TY - GEN

T1 - The approximability of maximum rooted triplets consistency with fan triplets and forbidden triplets

AU - Jansson, Jesper Andreas

AU - Lingas, Andrzej

AU - Lundell, Eva Marta

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The maximum rooted resolved triplets consistency problem takes as input a set R of resolved triplets and asks for a rooted phylogenetic tree that is consistent with the maximum number of elements in R. This paper studies the polynomial-time approximability of a generalization of the problem where in addition to resolved triplets, the input may contain fan triplets and forbidden triplets. To begin with, we observe that the generalized problem admits a 1/4-approximation in polynomial time. Next, we present a polynomial-time approximation scheme (PTAS) for dense instances based on smooth polynomial integer programming. Finally, we generalize Wu’s exact exponential-time algorithm in [19] for the original problem to also allow fan triplets, forbidden resolved triplets, and forbidden fan triplets. Forcing the algorithm to always output a k-ary phylogenetic tree for any specified k ≥ 2 then leads to an exponential-time approximation scheme (ETAS) for the generalized, unrestricted problem.

AB - The maximum rooted resolved triplets consistency problem takes as input a set R of resolved triplets and asks for a rooted phylogenetic tree that is consistent with the maximum number of elements in R. This paper studies the polynomial-time approximability of a generalization of the problem where in addition to resolved triplets, the input may contain fan triplets and forbidden triplets. To begin with, we observe that the generalized problem admits a 1/4-approximation in polynomial time. Next, we present a polynomial-time approximation scheme (PTAS) for dense instances based on smooth polynomial integer programming. Finally, we generalize Wu’s exact exponential-time algorithm in [19] for the original problem to also allow fan triplets, forbidden resolved triplets, and forbidden fan triplets. Forcing the algorithm to always output a k-ary phylogenetic tree for any specified k ≥ 2 then leads to an exponential-time approximation scheme (ETAS) for the generalized, unrestricted problem.

KW - Approximation algorithms

KW - Bioinformatics

KW - Phylogenetic tree

KW - Rooted triplet

KW - Smooth integer program

UR - http://www.scopus.com/inward/record.url?scp=84948951201&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-19929-0_23

DO - 10.1007/978-3-319-19929-0_23

M3 - Conference article published in proceeding or book

SN - 9783319199283

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 272

EP - 283

BT - Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings

PB - Springer Verlag

T2 - 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015

Y2 - 29 June 2015 through 1 July 2015

ER -