Probabilistic analysis of algorithms
Probabilistic analysis of algorithms
A threshold for unsatisfiability
Journal of Computer and System Sciences
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
A Polylogarithmic Approximation of the Minimum Bisection
SIAM Journal on Computing
The Asymptotic Order of the Random k -SAT Threshold
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The threshold for random k-SAT is 2k (ln 2 - O(k))
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the Maximum Satisfiability of Random Formulas
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Combinatorics, Probability and Computing
The Largest Eigenvalue of Sparse Random Graphs
Combinatorics, Probability and Computing
Exact and approximative algorithms for coloring G(n,p)
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Random MAX SAT, random MAX CUT, and their phase transitions
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part II
Max k-cut and approximating the chromatic number of random graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
The Lovász Number of Random Graphs
Combinatorics, Probability and Computing
Solving random satisfiable 3CNF formulas in expected polynomial time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
MAX k-CUT and approximating the chromatic number of random graphs
Random Structures & Algorithms
Strong Refutation Heuristics for Random k-SAT
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
On approximation of new optimization methods for assessing network vulnerability
INFOCOM'10 Proceedings of the 29th conference on Information communications
On the hardness and easiness of random 4-SAT formulas
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
| Hi-index | 5.23 |
We apply techniques from the theory of approximation algorithms to the problem of deciding whether a random k-SAT formula is satisfiable. Let Form n,k,m denote a random k-SAT instance with n variables and m clauses. Using known approximation algorithms for MAX CUT or MIN BISECTION, we show how to certify that Formn,4,m is unsatisfiable efficiently, provided that m ≥ Cn2 for a sufficiently large constant C 0. In addition, we present an algorithm based on the Lovász υ' function that decides within polynomial expected time whether Formn,k,m is satisfiable, provided that k is even and m ≥ C ċ 4knk/2. Finally, we present an algorithm that approximates random MAX 2-SAT on input Formn,2,m within a factor of 1 - O(n/m)1/2 in expected polynomial time. for m ≥ Cn.