The number of maximal independent sets in a connected graph
Discrete Mathematics
On generating all maximal independent sets
Information Processing Letters
Information Processing Letters
Acta Informatica
The number of maximal independent sets in triangle-free graphs
SIAM Journal on Discrete Mathematics
Recognition of q-Horn formulae in linear time
Discrete Applied Mathematics
Maximal independent sets in graphs with at most one cycle
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Worst case bounds for some NP-Complete modified Horn-SAT problems
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Parameterized Complexity
On Some Aspects of Mixed Horn Formulas
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Algorithms for variable-weighted 2-SAT and dual problems
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
A new bound for an NP-hard subclass of 3-SAT using backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A CNF class generalizing exact linear formulas
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A satisfiability-based approach for embedding generalized tanglegrams on level graphs
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Generalized k-ary tanglegrams on level graphs: A satisfiability-based approach and its evaluation
Discrete Applied Mathematics
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In this paper the class of mixed Horn formulas is introduced that contain a Horn part and a 2-CNF (conjunctive normal form) (also called quadratic) part. We show that SAT remains NP-complete for such instances and also that any CNF formula can be encoded in terms of a mixed Horn formula in polynomial time. Further, we provide an exact deterministic algorithm showing that SAT for mixed Horn formulas containing n variables is solvable in time O(2^0^.^5^2^8^4^n). A strong argument showing that it is hard to improve a time bound of O(2^n^/^2) for mixed Horn formulas is provided. We also obtain a fixed-parameter tractability classification for SAT restricted to mixed Horn formulas C of at most k variables in its positive 2-CNF part providing the bound O(@?C@?2^0^.^5^2^8^4^k). We further show that the NP-hard optimization problem minimum weight SAT for mixed Horn formulas can be solved in time O(2^0^.^5^2^8^4^n) if non-negative weights are assigned to the variables. Motivating examples for mixed Horn formulas are level graph formulas [B. Randerath, E. Speckenmeyer, E. Boros, P. Hammer, A. Kogan, K. Makino, B. Simeone, O. Cepek, A satisfiability formulation of problems on level graphs, ENDM 9 (2001)] and graph colorability formulas.