Communication complexity

Hiring! I am looking for a motivated and mathematically inclined PhD student with previous experience in courses/modules in theoretical computer science. This position is based in the Department of Computer Science in the University of Sheffield and comes with full tuition fee and stipend.

We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up to poly-logarithmic factors in five models of computation: the two-party communication, AND query, OR query, XOR query, and quantum edge query models.

We show a deterministic simulation (or lifting) theorem for composed problems $f \circ \mathsf{Eq}_n$ where the inner function (the gadget) is Equality on $n$ bits. When $f$ is a total function on $p$ bits, it is easy to show via a rank argument that the communication complexity of $f\circ \mathsf{Eq}_n$ is $\Omega(deg(f) \cdot n)$.

We develop a technique for proving lower bounds in the setting of asymmetric communication, a model that was introduced in the famous works of Miltersen (STOC'94) and Miltersen, Nisan, Safra and Wigderson (STOC'95).

We consider the problem of elimination in communication complexity, that was first raised by Ambainis et al. and later studied by Beimel et al. for its connection to the famous direct sum question.

We consider the point-to-point message passing model of communication in which there are $k$ processors with individual private inputs, each $n$-bit long. Each processor is located at the node of an underlying undirected graph and has access to private random coins.