In the gap Hamming distance problem, two parties must
determine whether their respective strings $x,y\in\{0,1\}^n$
are at Hamming distance less than $n/2-\sqrt n$ or greater
than $n/2+\sqrt n.$ In a recent tour de force, Chakrabarti and
Regev (STOC '11) proved the long-conjectured $\Omega(n)$ bound
on the randomized communication ... more >>>

We study the communication complexity of evaluating functions when the input data is randomly allocated (according to some known distribution) amongst two or more players, possibly with information overlap. This naturally extends previously studied variable partition models such as the best-case and worst-case partition models. We aim to understand whether ... more >>>

An $m$-variate polynomial $f$ is said to be an affine projection of some $n$-variate polynomial $g$ if there exists an $n \times m$ matrix $A$ and an $n$-dimensional vector $b$ such that $f(x) = g(A x + b)$. In other words, if $f$ can be obtained by replacing each variable ... more >>>