Average case complete problems
SIAM Journal on Computing
Information Sciences: an International Journal
On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A spectral technique for random satisfiable 3CNF formulas
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Scaling Properties of Pure Random Walk on Random 3-SAT
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
On smoothed analysis in dense graphs and formulas
Random Structures & Algorithms
Linear Upper Bounds for Random Walk on Small Density Random $3$-CNFs
SIAM Journal on Computing
Refuting Smoothed 3CNF Formulas
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Smoothed Analysis of Balancing Networks
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
A Better Algorithm for Random k-SAT
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A Better Algorithm for Random $k$-SAT
SIAM Journal on Computing
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
| Hi-index | 0.01 |
In this paper we study the model of ε-smoothed k-CNF formulas. Starting from an arbitrary instance F with n variables and m = dn clauses, apply the ε-smoothing operation of flipping the polarity of every literal in every clause independently at random with probability ε. Keeping ε and k fixed, and letting the density d = m/n grow, it is rather easy to see that for d ≥ ε-k ln 2, F becomes whp unsatisfiable after smoothing. We show that a lower density that behaves roughly like ε-k+1 suffices for this purpose. We also show that our bound on d is nearly best possible in the sense that there are k-CNF formulas F of slightly lower density that whp remain satisfiable after smoothing. One consequence of our proof is a new lower bound of Ω(2k/k2) on the density up to which Walksat solves random k-CNFs in polynomial time whp. We are not aware of any previous rigorous analysis showing that Walksat is successful at densities that are increasing as a function of k.