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Almost-polynomial ratio ETH-hardness of approximating densest k-subgraph
TLDR
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.
On Deep Learning with Label Differential Privacy
TLDR
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).
A Birthday Repetition Theorem and Complexity of Approximating Dense CSPs
TLDR
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.
An Improved Integrality Gap for the Călinescu-Karloff-Rabani Relaxation for Multiway Cut
TLDR
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.
On the parameterized complexity of approximating dominating set
TLDR
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.
Inapproximability of Maximum Biclique Problems, Minimum k-Cut and Densest At-Least-k-Subgraph from the Small Set Expansion Hypothesis
TLDR
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.
Parameterized Intractability of Even Set and Shortest Vector Problem from Gap-ETH
TLDR
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.
ETH-Hardness of Approximating 2-CSPs and Directed Steiner Network
TLDR
This question is answered positively by showing that no polynomial time algorithm can approximate 2-CSPs to within a factor of $|V|^{1 - o(1)}$.
Inapproximability of Maximum Edge Biclique, Maximum Balanced Biclique and Minimum k-Cut from the Small Set Expansion Hypothesis
TLDR
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.
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