We give a deterministic quasi-polynomial time algorithm for approximating the largest independent set in a graph. We show that if an $N$-vertex graph contains an independent set of size $2^{-t} N$, then we can find an independent set of size $2^t$ in quasi-polynomial time, for all $t$ up to a ... more >>>

Insertion sort is a basic algorithm for sorting permutations: it repeatedly cuts out one element and inserts it at its place among the elements sorted so far.
It sorts every permutation of length $n$ with at most $n-1$ such moves, and some permutations cannot be sorted with fewer ... more >>>

We establish an unconditional super-polynomial separation between quantum and classical PAC learning of Boolean functions under the uniform distribution in the large error regime. For every advantage $\lambda(n) = n^{-\omega(1)}$, we construct a concept class that a polynomial-time quantum learner learns to agreement $1/2+\lambda(n)$ with success probability at least $1-1/n^k$. ... more >>>