Additive approximation for near-perfect phylogeny construction

Pranjal Awasthi, Avrim Blum, Jamie Morgenstern, Or Sheffet

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings
Pages25-36
Number of pages12
DOIs
StatePublished - 2012
Externally publishedYes
Event15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 - Cambridge, MA, United States
Duration: 15 Aug 201217 Aug 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7408 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
Country/TerritoryUnited States
CityCambridge, MA
Period15/08/1217/08/12

Bibliographical note

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.

Fingerprint

Dive into the research topics of 'Additive approximation for near-perfect phylogeny construction'. Together they form a unique fingerprint.

Cite this