Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Property testers for dense constraint satisfaction programs on finite domains
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximating the Minimum Spanning Tree Weight in Sublinear Time
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Three theorems regarding testing graph properties
Random Structures & Algorithms
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximation Resistant Predicates from Pairwise Independence
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
An improved constant-time approximation algorithm for maximum~matchings
Proceedings of the forty-first annual ACM symposium on Theory of computing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Lower Bounds on Query Complexity for Testing Bounded-Degree CSPs
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Linear programming, width-1 CSPs, and robust satisfaction
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Testing the (s,t)-disconnectivity of graphs and digraphs
Theoretical Computer Science
Constant-Time approximation algorithms for the knapsack problem
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple semidefinite programming and a rounding scheme for it. In this paper, we show that similar results hold for constant-time approximation algorithms in the bounded-degree model. Specifically, we present the following: (i) For every CSP, we construct an oracle that serves an access, in constant time, to a nearly optimal solution to a basic LP relaxation of the CSP. (ii) Using the oracle, we give a constant-time rounding scheme that achieves an approximation ratio coincident with the integrality gap of the basic LP. (iii) Finally, we give a generic conversion from integrality gaps of basic LPs to hardness results. All of those results are unconditional. Therefore, for every bounded-degree CSP, we give the best constant-time approximation algorithm among all. A CSP instance is called ε-far from satisfiability if we must remove at least an ε-fraction of constraints to make it satisfiable. A CSP is called testable if there is a constant-time algorithm that distinguishes satisfiable instances from ε-far instances with probability at least 2/3. Using the results above, we also derive, under a technical assumption, an equivalent condition under which a CSP is testable in the bounded-degree model.