A theoretical analysis of backtracking in the graph coloring problem
Journal of Algorithms
The solution of some random NP-hard problems in polynomial expected time
Journal of Algorithms
On the greedy algorithm for satisfiability
Information Processing Letters
Coloring random and semi-random k-colorable graphs
Journal of Algorithms
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Finding a large hidden clique in a random graph
proceedings of the eighth international conference on Random structures and algorithms
Finding and certifying a large hidden clique in a semirandom graph
Random Structures & Algorithms
A spectral technique for random satisfiable 3CNF formulas
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Coupon Collectors, q-Binomial Coefficients and the Unsatisfiability Threshold
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Colouring Random Graphs in Expected Polynomial Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Coloring Random Graphs in Polynomial Expected Time
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Finding Large Independent Sets in Polynomial Expected Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Random knapsack in expected polynomial time
Journal of Computer and System Sciences - Special issue: STOC 2003
Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT
Theoretical Computer Science
Performance test of local search algorithms using new types of random CNF formulas
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Coloring sparse random k-colorable graphs in polynomial expected time
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
On the Security of Goldreich's One-Way Function
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the random satisfiable process
Combinatorics, Probability and Computing
A spectral method for MAX2SAT in the planted solution model
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
| Hi-index | 0.00 |
We present an algorithm for solving 3SAT instances. Several algorithms have been proved to work whp (with high probability) for various SAT distributions. However, an algorithm that works whp has a drawback. Indeed for typical instances it works well, however for some rare inputs it does not provide a solution at all. Alternatively, one could require that the algorithm always produce a correct answer but perform well on average. Expected polynomial time formalizes this notion. We prove that for some natural distribution on 3CNF formulas, called planted 3SAT, our algorithm has expected polynomial (in fact, almost linear) running time. The planted 3SAT distribution is the set of satisfiable 3CNF formulas generated in the following manner. First, a truth assignment is picked uniformly at random. Then, each clause satisfied by it is included in the formula with probability p. Extending previous work for the planted 3SAT distribution, we present, for the first time for a satisfiable SAT distribution, an expected polynomial time algorithm. Namely, it solves all 3SAT instances, and over the planted distribution (with p = d/n2, d 0 a sufficiently large constant) it runs in expected polynomial time. Our results extend to k-SAT for any constant k.