Packet scheduling over a switch (interconnect) fabric is a wellstudied problem in distributed computing, with known near-optimal distributed bipartite matching based protocols.

We present Sincronia, a near-optimal network design for coflows that can be implemented on top on any transport layer (for flows) that supports priority scheduling. Sincronia achieves this using a key technical result --- we show that given a "right" ordering of coflows, any per-flow rate allocation mechanism achieves average coflow completion time within 4X of the optimal as long as (co)flows are prioritized with respect to the ordering.

The problem of three-party secure computation, where a function of private data of two parties is to be computed by a third party without revealing information beyond respective inputs or outputs is considered. New and better lower bounds on the amount of communication required between the parties to guarantee zero probability of error in the computation and achieve information-theoretic security are derived. Protocols are presented and proved to be optimal in some cases by showing that they achieve the improved lower bounds.