A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Inapproximability Results for Vertex Cover on k -Uniform Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the Power of Unique 2-Prover 1-Round Games
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Asymmetric k-center is log* n-hard to approximate
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Minimizing Average Flow-time: Upper and Lower Bounds
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of 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
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
Gaussian Bounds for Noise Correlation of Functions and Tight Analysis of Long Codes
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Optimal Long Code Test with One Free Bit
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Nearly optimal NP-hardness of vertex cover on k-uniform k-partite hypergraphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proceedings of the 5th conference on Innovations in theoretical computer science
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In a beautiful result, Raghavendra established optimal Unique Games Conjecture (UGC)-based inapproximability for a large class of constraint satisfaction problems (CSPs). In the class of CSPs he considers, of which Maximum Cut is a prominent example, the goal is to find an assignment which maximizes a weighted fraction of constraints satisfied. He gave a generic semi-definite program (SDP) for this class of problems and showed how the approximability of each problem is determined by the corresponding SDP (upto an arbitrarily small additive error) assuming the UGC. He noted that his techniques do no apply to CSPs with strict constraints (all of which must be satisfied) such as Vertex Cover. In this paper we address the approximability of these strict-CSPs. In the class of CSPs we consider, one is given a set of constraints over a set of variables, and a cost function over the assignments, the goal is to find an assignment to the variables of minimum cost which satisfies all the constraints. We present a generic linear program (LP) for a large class of strict-CSPs and give a systematic way to convert integrality gaps for this LP into UGC-based inapproximability results. Some important problems whose approximability our framework captures are Vertex Cover, Hypergraph Vertex Cover, k-partite-Hypergraph Vertex Cover, Independent Set and other covering and packing problems over q-ary alphabets, and a scheduling problem. For the covering and packing problems, which occur quite commonly in practice as well, we provide a matching rounding algorithm, thus settling their approximability upto an arbitrarily small additive error.