On the expressive power of Datalog: tools and a case study
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Regular Article: Extension Operations on Sets of Leaf-Labeled Trees
Advances in Applied Mathematics
Conjunctive-query containment and constraint satisfaction
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The difficulty of constructing a leaf-labelled tree including or avoiding given subtrees
Discrete Applied Mathematics
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Point algebras for temporal reasoning: algorithms and complexity
Artificial Intelligence
Relation Algebras and their Application in Temporal and Spatial Reasoning
Artificial Intelligence Review
Determining the consistency of partial tree descriptions
Artificial Intelligence
Constraint Satisfaction Problems with Infinite Templates
Complexity of Constraints
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Hi-index | 0.00 |
Several computational problems in phylogenetic reconstruction can be formulated as restrictions of the following general problem: given a formula in conjunctive normal form where the atomic formulas are rooted triples, is there a rooted binary tree that satisfies the formula? If the formulas do not contain disjunctions and negations, the problem becomes the famous rooted triple consistency problem, which can be solved in polynomial time by an algorithm of Aho, Sagiv, Szymanski, and Ullman. If the clauses in the formulas are restricted to disjunctions of negated triples, Ng, Steel, and Wormald showed that the problem remains NP-complete. We systematically study the computational complexity of the problem for all such restrictions of the clauses in the input formula. For certain restricted disjunctions of triples we present an algorithm that has sub-quadratic running time and is asymptotically as fast as the fastest known algorithm for the rooted triple consistency problem. We also show that any restriction of the general rooted phylogeny problem that does not fall into our tractable class is NP-complete, using known results about the complexity of Boolean constraint satisfaction problems. Finally, we present a pebble game argument that shows that the rooted triple consistency problem (and also all generalizations studied in this paper) cannot be solved by Datalog.