The Stellar tree: a Compact Representation for Simplicial Complexes and Beyond

The efficient representation and management of simplicial and cell complexes is an active research topic in several fields, including geometric modeling, computer graphics, scientific visualization, and geographic data processing. In this paper, we propose the Stellar tree, a topological data structure for performing efficient topological queries on simplicial and non-simplicial complexes. We prove that a Stellar tree provides a scalable, compact and flexible data structure to represent these complexes, using a fraction of the memory required by a corresponding topological data structure on the global complex.