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We consider the problem of efficiently computing a discrete Morse complex onsimplicial complexes of arbitrary dimension and very large size. Based on acommon graph-based formalism, we analyze existing data structures forsimplicial complexes, and we define an efficient encoding for the discreteMorse gradient on the most compact of such representations. We theoreticallycompare methods based on reductions and coreductions for computing a discreteMorse gradient, proving that the combination of reductions and coreductionsproduces new mutually equivalent approaches. We design and implement a newalgorithm for computing a discrete Morse complex on simplicial complexes. Weshow that our approach scales very well with the size and the dimension of thesimplicial complex also through comparisons with the only existingpublic-domain algorithm for discrete Morse complex computation. We discussapplications to the computation of multi-parameter persistent homology and ofextrema graphs for visualization of time-varying 3D scalar fields.

Computing discrete Morse complexes from simplicial complexes