Distributed Computing on Core-Periphery Networks: Axiom-based Design

Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms and is robust and efficient in number of links. Rather than providing a concrete network model, we take an axiom-based design approach. We provide three intuitive (and independent) algorithmic axioms and prove that any network that satisfies all axioms enjoys an efficient algorithm for a range of tasks (e.g., MST, sparse matrix multiplication, etc.). We also show the minimality of our axiom set: for networks that satisfy any subset of the axioms, the same efficiency cannot be guaranteed for \emph{any} deterministic algorithm.