Distributed Computation of Persistent Homology

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems, we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 10GB of memory per node. ∗Institute of Science and Technology Austria, Klosterneuburg, Austria. http://ulrich-bauer.org †Max-Planck-Center for Visual Computing and Communication, Saarbrücken, Germany. http://mpi-inf.mpg.de/ ̃mkerber ‡Institute of Science and Technology Austria, Klosterneuburg, Austria. http://ist.ac.at/ ̃reininghaus ar X iv :1 31 0. 07 10 v1 [ cs .C G ] 2 O ct 2 01 3