Triangulating 3-colored graphs
SIAM Journal on Discrete Mathematics
Complexity and algorithms for reasoning about time: a graph-theoretic approach
Journal of the ACM (JACM)
Triangulating Vertex-Colored Graphs
SIAM Journal on Discrete Mathematics
Complexity of generalized satisfiability counting problems
Information and Computation
Algorithmic aspects of tree amalgamation
Journal of Algorithms
A characterization for a set of partial partitions to define an X-tree
Discrete Mathematics
Dichotomy Theorem for the Generalized Unique Satisfiability Problem
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
Theoretical Computer Science
Theoretical Computer Science
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
The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
| Hi-index | 5.23 |
A phylogeny is a tree capturing evolution and ancestral relationships of a set of taxa (e.g., species). Reconstructing phylogenies from molecular data plays an important role in many areas of contemporary biological research. A phylogeny is perfect if (in rough terms) it correctly captures all input data. Determining if a perfect phylogeny exists was shown to be intractable in 1992 by Mike Steel (Steel, 1992) [32] and independently by Bodlaender et al. (Bodlaender et al., 1992) [4]. In light of this, a related problem was proposed by Steel (1992) [32]: given a perfect phylogeny, determine if it is the unique perfect phylogeny for the given dataset, where the dataset is provided as a set of quartet (4-leaf) trees. It was suggested that this problem may be more tractable (Steel, 1992) [32], and determining its complexity became known as the Quartet Challenge (Steel, 2012) [33]. In this paper, we resolve this question by showing that the problem is CoNP-complete. We prove this by relating perfect phylogenies to satisfying assignments of Boolean formulae. To this end, we cast the question as a chordal sandwich problem. As a particular consequence of our method, we show that the unique minimal chordal sandwich problem is CoNP-complete, and counting minimal chordal sandwiches is #P-complete.