TY - GEN
T1 - Additive approximation for near-perfect phylogeny construction
AU - Awasthi, Pranjal
AU - Blum, Avrim
AU - Morgenstern, Jamie
AU - Sheffet, Or
N1 - Funding Information: This work was supported in part by the National Science Foundation under grant CCF-1116892, by an NSF Graduate Fellowship, and by the MSR-CMU Center for Computational Thinking.
PY - 2012
Y1 - 2012
N2 - We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on n points over the Boolean hypercube of dimension d. It is known that an optimal tree can be found in linear time [1] if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly d. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is d + q, it is known [2] that an exact solution can be found in running time which is polynomial in the number of species and d, yet exponential in q. In this work, we give a polynomial-time algorithm (in both d and q) that finds a phylogenetic tree of cost d + O(q 2). This provides the best guarantees known-namely, a (1 + o(1))-approximation-for the case log(d) ≪ q ≪ √d, broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations.
AB - We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on n points over the Boolean hypercube of dimension d. It is known that an optimal tree can be found in linear time [1] if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly d. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is d + q, it is known [2] that an exact solution can be found in running time which is polynomial in the number of species and d, yet exponential in q. In this work, we give a polynomial-time algorithm (in both d and q) that finds a phylogenetic tree of cost d + O(q 2). This provides the best guarantees known-namely, a (1 + o(1))-approximation-for the case log(d) ≪ q ≪ √d, broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations.
UR - http://www.scopus.com/inward/record.url?scp=84865281325&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-32512-0_3
DO - 10.1007/978-3-642-32512-0_3
M3 - منشور من مؤتمر
SN - 9783642325113
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 25
EP - 36
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
Y2 - 15 August 2012 through 17 August 2012
ER -