On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
SIAM Journal on Computing
A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
Efficient algorithms for inverting evolution
Journal of the ACM (JACM)
Absolute convergence: true trees from short sequences
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Fast recovery of evolutionary trees with thousands of nodes
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Inferring Evolutionary Trees with Strong Combinatorial Evidence
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
Nearly tight bounds on the learnability of evolution
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Evolutionary Trees can be Learned in Polynomial Time in the Two-State General Markov Model
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Nearly tight bounds on the learnability of evolution
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Theoretical Computer Science
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
| Hi-index | 0.02 |
This paper treats polynomial-time algorithms for reconstruction of phylogenetic trees. The disc-covering method (DCM) presented by Huson et al. (J. Comput. Biol. 6 (3/4) (1999) 369) is a method that boosts the performance of phylogenetic tree construction algorithms. Actually, they gave two variations of DCM-Buneman. The first variation was guaranteed to recover the true tree with high probability from polynomial-length sequences (i.e. polynomial in the number of given taxa), but it was not proven to run in polynomial time. The second variation was guaranteed to run in polynomial time. However, it is a heuristic in the sense that it was not proven to recover the true tree with high probability from polynomial-length sequences.We present an improved DCM. The difference between our improved DCM and the heuristic variation of the original DCM is marginal. The main contribution of this paper is the analysis of the algorithm. Our analysis shows that the improved DCM combines the desirable properties of the two variations of the original DCM. That is, it runs in polynomial time and it recovers the true tree with high probability from polynomial-length sequences. Moreover, this is true when the improved DCM is applied to the Neighbor-Joining, the Buneman, as well as the Agarwala algorithm. A key observation for the result of Huson et al. was that threshold graphs of additive distance functions are chordal. We prove a chordal graph theorem concerning minimal triangulations of threshold graphs constructed from distance functions which are close to being additive. This theorem is the key observation behind our improved DCM and it may be interesting in its own right.