It is shown, assuming the exponential time hypothesis (ETH), that there is no polynomial-time algorithm that approximates Densest k-Subgraph to within n1/(loglogn)c factor of the optimum, where c > 0 is a universal constant independent of n.Expand

A novel algorithm, Randomized Response with Prior (RRWithPrior), is proposed, which can provide more accurate results while maintaining the same level of privacy guaranteed by RR, and is applied to learn neural networks with label differential privacy (LabelDP).Expand

The birthday repetition theorem implies that any algorithm that approximates fully-dense Max $k-CSP to within a $q^{1/i}$ factor takes $(nq)^{\tilde \Omega_k(i)}$ time, almost tightly matching the algorithmic result based on Sherali-Adams relaxation.Expand

An improved integrality gap instance for the Călinescu-Karloff-Rabani LP relaxation of the Multiway Cut problem is constructed, which implies Unique Games hardness of approximating Multiway cut of the same ratio.Expand

To prove hardness of approximation of a certain parameterized variant of the label cover problem, it suffices to devise a specific protocol for a communication problem that depends on which hypothesis the authors rely on, generalizing the ideas from a recent breakthrough work of Abboud et al.Expand

Conditional inapproximability results with essentially optimal ratios for the following graph problems based on the Small Set Expansion Hypothesis are proved: Maximum Edge Biclique, Maximum Balanced Bicles, Minimum k-Cut and Densest At-Least-k-Subgraph.Expand

This work shows that, for any $p > 1$, $k-SVP is hard to approximate (in FPT time) to some constant factor, assuming PIH, and considers the parameterized $k$-Shortest Vector Problem, which is also a long-standing open problem in the field of Parameterized Complexity.Expand

Conditional inapproximability results are proved for the following graph problems based on the Small Set Expansion Hypothesis by combining a technique developed by Raghavendra, Steurer and Tulsiani and a generalization of Bansal and Khot's long code test.Expand