TY - GEN
T1 - A linear time approximation scheme for maximum quartet consistency on sparse sampled inputs
AU - Snir, Sagi
AU - Yuster, Raphael
PY - 2011
Y1 - 2011
N2 - Phylogenetic tree reconstruction is a fundamental biological problem. Quartet amalgamation - combining a set of trees over four taxa into a tree over the full set - stands at the heart of many phylogenetic reconstruction methods. However, even reconstruction from a consistent set of quartet trees, i.e. all quartets agree with some tree, is NP-hard, and the best approximation ratio known is 1/3. For a dense input of Θ(n4) quartets (not necessarily consistent), the problem has a polynomial time approximation scheme. When the number of taxa grows, considering such dense inputs is impractical and some sampling approach is imperative. In this paper we show that if the number of quartets sampled is at least Θ(n2 log n), there is a randomized approximation scheme, that runs in linear time in the number of quartets. The previously known polynomial approximation scheme for that problem required a very dense sample of size Θ(n4). We note that samples of size Θ(n2 log n) are sparse in the full quartet set.
AB - Phylogenetic tree reconstruction is a fundamental biological problem. Quartet amalgamation - combining a set of trees over four taxa into a tree over the full set - stands at the heart of many phylogenetic reconstruction methods. However, even reconstruction from a consistent set of quartet trees, i.e. all quartets agree with some tree, is NP-hard, and the best approximation ratio known is 1/3. For a dense input of Θ(n4) quartets (not necessarily consistent), the problem has a polynomial time approximation scheme. When the number of taxa grows, considering such dense inputs is impractical and some sampling approach is imperative. In this paper we show that if the number of quartets sampled is at least Θ(n2 log n), there is a randomized approximation scheme, that runs in linear time in the number of quartets. The previously known polynomial approximation scheme for that problem required a very dense sample of size Θ(n4). We note that samples of size Θ(n2 log n) are sparse in the full quartet set.
UR - http://www.scopus.com/inward/record.url?scp=80052364613&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-22935-0_29
DO - 10.1007/978-3-642-22935-0_29
M3 - Conference contribution
SN - 9783642229343
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 339
EP - 350
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Y2 - 17 August 2011 through 19 August 2011
ER -