On fixed-parameter tractability and approximability of NP optimization problems
Journal of Computer and System Sciences - special issue on complexity theory
Reactive search, a history-sensitive heuristic for MAX-SAT
Journal of Experimental Algorithmics (JEA)
An improved fixed-parameter algorithm for vertex cover
Information Processing Letters
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Satisfiability - Algorithms and Logic
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Some Prospects for Efficient Fixed Parameter Algorithms
SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Faster Exact Solutions for MAX2SAT
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
New bounds for MAX-SAT by clause learning
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
A new algorithm for parameterized MAX-SAT
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
| Hi-index | 0.00 |
Given a boolean formula F in conjunctive normal form and an integer k, is there a truth assignment satisfying at least k clauses? This is the decision version of the Maximum Satisfiability (MaxSat) problem we study in this paper. We improve upper bounds on the worst case running time for MaxSat. First, Cai and Chen showed that MaxSat can be solved in time |F|2O(k) when the clause size is bounded by a constant. Imposing no restrictions on clause size, Mahajan and Raman and, independently, Dantsin et al. improved this to O(|F|Φk), where Φ ≅ 1:6181 is the golden ratio. We present an algorithm running in time O(|F|1:3995k). The result extends to finding an optimal assignment and has several applications, in particular, for parameterized complexity and approximation algorithms. Moreover, if F has K clauses, we can find an optimal assignment in O(|F|1:3972K) steps and in O(1:1279|F|) steps, respectively. These are the fastest algorithm in the number of clauses and the length of the formula, respectively.