We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In particular, we prove the best known lower bound for TSP with ... more >>>

A family of Boolean circuits $\{C_n\}_{n\geq 0}$ is called \emph{$\gamma(n)$-weakly uniform} if
there is a polynomial-time algorithm for deciding the direct-connection language of every $C_n$,
given \emph{advice} of size $\gamma(n)$. This is a relaxation of the usual notion of uniformity, which allows one
to interpolate between complete uniformity (when $\gamma(n)=0$) ... more >>>

Given a set of $n$ random $d$-dimensional boolean vectors with the promise that two of them are $\rho$-correlated with each other, how quickly can one find the two correlated vectors? We present a surprising and simple algorithm which, for any constant $\epsilon>0$ runs in (expected) time $d n^{\frac{3 \omega}{4}+\epsilon} poly(\frac{1}{\rho})< ... more >>>