On a conjecture about compatibility of multi-states characters

Authors:
Michel Habib;Thu-Hien To
Affiliations:
Université Paris Diderot-Paris 7, LIAFA, Paris Cedex 13, France;Université Paris Diderot-Paris 7, LIAFA, Paris Cedex 13, France
Venue:
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Year:
2011

Citing 13
Cited 1

Inferring Evolutionary History from DNA Sequences

SIAM Journal on Computing
A Polynomial-Time Algorithm for the Perfect Phylogeny Problem when the Number of Character States is Fixed

SIAM Journal on Computing
Graph sandwich problems

Journal of Algorithms
Triangulating vertex colored graphs

SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A fast algorithm for the computation and enumeration of perfect phylogenies when the number of character states is fixed

Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Tree Reconstruction from Multi-State Characters

Advances in Applied Mathematics
Two Strikes Against Perfect Phylogeny

ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Four Characters Suffice to Convexly Define a Phylogenetic Tree

SIAM Journal on Discrete Mathematics
Optimal, efficient reconstruction of root-unknown phylogenetic networks with constrained and structured recombination

Journal of Computer and System Sciences - Special issue on bioinformatics II
The Fine Structure of Galls in Phylogenetic Networks

INFORMS Journal on Computing
Generalizing the four gamete condition and splits equivalence theorem: perfect phylogeny on three state characters

WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Unique perfect phylogeny is NP-hard

CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Integer programming formulations and computations solving phylogenetic and population genetic problems with missing or genotypic data

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics

Improved lower bounds on the compatibility of quartets, triplets, and multi-state characters

WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Perfect phylogeny consisting of determining the compatibility of a set of characters is known to be NP-complete [4,28]. We propose in this article a conjecture on the necessary and sufficient conditions of compatibility: Given a set C of r-states full characters, there exists a function f(r) such that C is compatible iff every set of f(r) characters of C is compatible. According to [7,9,8,25,11,23], f(2) = 2, f(3) = 3 and f(r) ≥ r. [23] conjectured that f(r) = r for any r ≥ 2. In this paper, we present an example showing that f(4) ≥ 5. Therefore it could be the case that for r ≥ 4 characters the problem behavior drastically changes. In a second part, we propose a closure operation for chordal sandwich graphs. The later problem is a common approach of perfect phylogeny.