Additive approximation for near-perfect phylogeny construction

Pranjal Awasthi; Avrim Blum; Jamie Morgenstern; Or Sheffet

doi:10.1007/978-3-642-32512-0_3

Additive approximation for near-perfect phylogeny construction

Pranjal Awasthi
, Avrim Blum
, Jamie Morgenstern
, Or Sheffet

Carnegie Mellon University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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 language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings
Pages	25-36
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-32512-0_3
State	Published - 2012
Externally published	Yes
Event	15th 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 2012 → 17 Aug 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7408 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
Country/Territory	United States
City	Cambridge, MA
Period	15/08/12 → 17/08/12

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.

Funding

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.

Funders	Funder number
MSR-CMU Center for Computational Thinking
National Science Foundation	CCF-1116892
Directorate for Computer and Information Science and Engineering	1116892

Access to Document

10.1007/978-3-642-32512-0_3

Cite this

Awasthi, P., Blum, A., Morgenstern, J., & Sheffet, O. (2012). Additive approximation for near-perfect phylogeny construction. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings (pp. 25-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7408 LNCS). https://doi.org/10.1007/978-3-642-32512-0_3

Awasthi, Pranjal ; Blum, Avrim ; Morgenstern, Jamie et al. / Additive approximation for near-perfect phylogeny construction. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings. 2012. pp. 25-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

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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.; 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 ; Conference date: 15-08-2012 Through 17-08-2012",

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Awasthi, P, Blum, A, Morgenstern, J & Sheffet, O 2012, Additive approximation for near-perfect phylogeny construction. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7408 LNCS, pp. 25-36, 15th 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, 15/08/12. https://doi.org/10.1007/978-3-642-32512-0_3

Additive approximation for near-perfect phylogeny construction. / Awasthi, Pranjal; Blum, Avrim; Morgenstern, Jamie et al.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings. 2012. p. 25-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7408 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Awasthi P, Blum A, Morgenstern J, Sheffet O. Additive approximation for near-perfect phylogeny construction. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings. 2012. p. 25-36. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-32512-0_3

Additive approximation for near-perfect phylogeny construction

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