Before revision:  In this paper, we propose the Stellar tree, a topological data structure for performing efficient topological queries on simplicial and non-simplicial complexes .
After revision:  In this paper, we propose the Stellar tree, which combines a nested spatial tree with a simple tuning parameter to control the number of vertices in a region. Stellar trees exploit the complex's spatial locality by reordering vertex and cell indices according to the spatial decomposition and by compressing sequential ranges of indices. Stellar trees are competitive with state-of-the-art topological data structures for manifold simplicial complexes and offer significant improvements for cell complexes and non-simplicial complexes .