We consider the problem of efficiently constructing an as large as possible family of permutations such that each pair of permutations are far part (i.e., disagree on a constant fraction of their inputs).
Specifically, for every $n\in\N$, we present a collection of $N=N(n)=(n!)^{\Omega(1)}$ pairwise far apart permutations $\{\pi_i:[n]\to[n]\}_{i\in[N]}$ and ... more >>>

We show that there is a family of monotone multilinear polynomials over $n$ variables in VP, such that any monotone arithmetic circuit for it would be of size $2^{\Omega(n)}$. Before our result, strongly exponential lower bounds on the size of monotone circuits were known only for computing explicit polynomials in ... more >>>

We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial erasures in adjacency entries. We focus on two computational tasks: testing if a graph is connected ... more >>>