A polynomial algorithm for the 2-path problem for semicomplete digraphs
SIAM Journal on Discrete Mathematics
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
A Geometric Approach to Betweenness
SIAM Journal on Discrete Mathematics
Random sampling and approximation of MAX-CSP problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Tensor decomposition and approximation schemes for constraint satisfaction problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Additive Approximation for Edge-Deletion Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SIAM Journal on Discrete Mathematics
The Minimum Feedback Arc Set Problem is NP-Hard for Tournaments
Combinatorics, Probability and Computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On Random Ordering Constraints
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
On random betweenness constraints
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
On random betweenness constraints
Combinatorics, Probability and Computing
Approximation schemes for the betweenness problem in tournaments and related ranking problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Conflict packing yields linear vertex-kernels for k-FAST, k-dense RTI and a related problem
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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In the past decade, there has been a stream of work in designing approximation schemes for dense instances of NP-Hard problems. These include the work of Arora, Karger and Karpinski from 1995 and that of Frieze and Kannan from 1996. We address the problem of proving hardness results for (fully) dense problems, which has been neglected despite the fruitful effort put in upper bounds. In this work, we prove hardness results of dense instances of a broad family of CSP problems, as well as a broad family of ranking problems which we refer to as CSP-Rank. Our techniques involve a construction of a pseudorandom hypergraph coloring, which generalizes the well-known Paley graph, recently used by Alon to prove hardness of feedback arc-set in tournaments.