We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent ... more >>>

Abstract A map $f:{0,1}^{n}\to {0,1}^{n}$ has locality t if every output bit of f depends only on t input bits. Arora, Steurer, and Wigderson (2009) ask if there exist bounded-degree expander graphs on $2^{n}$ nodes such that the neighbors of a node $x\in {0,1}^{n}$ can be computed by maps of ... more >>>

We show that if gap-3SAT has no sub-exponential time algorithms then a weak form of the sliding scale conjecture holds. Namely, for every $\alpha>0$ any algorithm for $n^\alpha$-approximating the value of label cover must run in time at least $n^{\Omega(\exp(1/\alpha))}$, where $n$ is the size of the instance.

Put differently, ... more >>>