Finding cliques in random graphs and the closely related ``planted'' clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for t = ... more >>>

Consider a systematic linear code where some (local) parity symbols depend on few prescribed symbols, while other (heavy) parity symbols may depend on all data symbols. Local parities allow to quickly recover any single symbol when it is erased, while heavy parities provide tolerance to a large number of simultaneous ... more >>>

We design two deterministic polynomial time algorithms for variants of a problem introduced by Edmonds in 1967: determine the rank of a matrix $M$ whose entries are homogeneous linear polynomials over the integers. Given a linear subspace $\mathcal{B}$ of the $n \times n$ matrices over some field $\mathbb{F}$, we consider ... more >>>