Multicore Homology

4 We design and implement a framework for parallel computation of homology of cellular spaces over 5 field coefficients. We begin by cutting a space into local pieces. We then compute the homology of 6 each piece in parallel using the persistence algorithm. Finally we glue the pieces together by construct7 ing the Mayer-Vietoris blowup complex and computing its homology. Theoretically, we show that the 8 first step, optimal decomposition into local pieces is NP-HARD. In practice we use a decomposition 9 based on graph partitions, which produces decompositions with a simple structure and bounded over10 lap. We implement our algorithms for multicore computers, and demonstrate its efficacy with a suite 11 of experiments. For example, we achieve roughly an 8× speedup of the homology computations on a 12 3-dimensional complex with about 10 million simplices using 11 cores. 13 We include line numbers for our reviewers’ ease of reference. 14