Implications of forbidden structures for extremal algorithmic problems
Theoretical Computer Science
A guided tour of Chernoff bounds
Information Processing Letters
On the approximation of maximum satisfiability
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Randomized algorithms
Local and global relational consistency
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity of Partial Satisfaction
Journal of the ACM (JACM)
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Worst-case time bounds for coloring and satisfiability problems
Journal of Algorithms
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On Local Versus Global Satisfiability
SIAM Journal on Discrete Mathematics
Extremal Combinatorics: With Applications in Computer Science
Extremal Combinatorics: With Applications in Computer Science
Locally consistent constraint satisfaction problems with binary constraints
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Locally consistent constraint satisfaction problems with binary constraints
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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An instance of a constraint satisfaction problem is l-consistent if any l constraints of it can be simultaneously satisfied. For a set Π of constraint types ρl (Π) denotes the largest ratio of constraints which can be satisfied in any l-consistent instance composed by constraints of types from Π. In the case of sets Π consisting of finitely many Boolean predicates, we express the limit ρ∞ (Π) : =liml→∞ ρl(Π) as the minimum of a certain functional on a convex set of polynomials. Our results yield a robust deterministic algorithm (for a fixed set Π) running in time linear in the size of the input and 1/ε which finds either an inconsistent set of constraints (of size bounded by the function of ε) or a truth assignment which satisfies the fraction of at least ρ∞ (Π) - ε of the given constraints. We also compute the values of ρl ({P}) for several specific predicates P.