On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Deterministic Algorithms for k-SAT Based on Covering Codes and Local Search
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
A Probabilistic 3-SAT Algorithm Further Improved
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
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
FOCS '97 Proceedings of the 38th 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
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Improved upper bounds for 3-SAT
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
An improved exact algorithm for the domatic number problem
Information Processing Letters
An exact algorithm for the minimum dominating clique problem
Theoretical Computer Science
Efficient approximation of min set cover by moderately exponential algorithms
Theoretical Computer Science
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
An Improved SAT Algorithm in Terms of Formula Length
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Exponential time algorithms for the minimum dominating set problem on some graph classes
ACM Transactions on Algorithms (TALG)
Exact algorithms for edge domination
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
An exact algorithm for the Boolean connectivity problem for k-CNF
Theoretical Computer Science
Discrete Applied Mathematics
Exact algorithms for dominating set
Discrete Applied Mathematics
Algorithms and constraint programming
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Solving connected dominating set faster than 2n
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
An exact 2.9416n algorithm for the three domatic number problem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
An exact algorithm for the minimum dominating clique problem
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
An exact algorithm for the boolean connectivity problem for k-CNF
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Polynomial space algorithms for counting dominating sets and the domatic number
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Counting minimum weighted dominating sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Exponential algorithms, i.e. algorithms of complexity O(cn) for some c 1, seem to be unavoidable in the case of NP-complete problems (unless P=NP), especially if the problem in question needs to be solved exactly and not approximately. If the constant c is close to 1 such algorithms have practical importance. Deterministic algorithms of exponential complexity usually involve some kind of backtracking. The analysis of such backtracking algorithms in terms of solving recurrence equations is quite well understood. The purpose of the current paper is to show cases in which the constant c could be significantly reduced, and to point out that there are some randomized exponential-time algorithms which use randomization in some new ways. Most of our examples refer to the 3-SAT problem, i.e. the problem of determining satisfiability of formulas in conjunctive normal form with at most 3 literals per clause.