Per Austrin

Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs

We study the inapproximability of Vertex Cover and Independent Set on degree

Balanced max 2-sat might not be the hardest

d

Towards Sharp Inapproximability for Any 2-CSP

graphs. We prove that: \begin{itemize} \item Vertex Cover is Unique Games-hard to approximate to within a factor

On the usefulness of predicates

2 - (2+o_d(1)) \frac{ \log\log d}{ \log d}

Inapproximability of vertex cover and independent set in bounded degree graphs

. This exactly matches the algorithmic result of Halperin \cite{halperin02improved} up to the

Better Balance by Being Biased: A 0.8776-Approximation for Max Bisection

o_d(1)

Inapproximability of treewidth, one-shot pebbling, and related layout problems

term. \item Independent Set is Unique Games-hard to approximate to within a factor

Inapproximability of Treewidth and Related Problems

O(\frac{d}{\log^2 d})

On the Usefulness of Predicates

. This improves the

On the impossibility of cryptography with tamperable randomness

\frac{d}{\log^{O(1)}(d)}