Notes on the distributed computation of merge trees on CW-complexes

Merge trees are topological structures that record changes in super-level set topology of a scalar function. They encapsulate a wide range of threshold based features which can be extracted for analysis and visualization. Several distributed and parallel algorithms for computing merge trees have been proposed in the past, but they are restricted to simplicial complexes or regular grids. In this paper, we present an algorithm for the distributed computation of merge trees on CW-complexes. The conditions on the CW-complex required for the computation of the merge tree are discussed alongside a proof of correctness.