Research output per year
Research output per year
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
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(n^{4}) 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(n^{2} 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(n^{4}). We note that samples of size Θ(n^{2} log n) are sparse in the full quartet set.
Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |
Subtitle of host publication | Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings |
Pages | 339-350 |
Number of pages | 12 |
DOIs | |
State | Published - 2011 |
Event | 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States Duration: 17 Aug 2011 → 19 Aug 2011 |
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6845 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference | 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 |
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Country/Territory | United States |
City | Princeton, NJ |
Period | 17/08/11 → 19/08/11 |
Research output: Contribution to journal › Article › peer-review