Persistent Homology is a computational method of data mining in the field of Topological Data Analysis. Large-scale data analysis with persistent homology is computationally expensive and memory intensive. The performance of persistent homology has been rigorously studied to optimize data encoding and intermediate data structures for high-performance computation. This paper provides an application-centric survey of the High-Performance Computation of Persistent Homology. Computational topology concepts are reviewed and detailed for a broad data science and engineering audience.

In recent years genetic data analysis has seen a rapid increase in the scale of data to be analyzed. Schadt et al (NRG 11:647–657, 2010) offered that with data sets approaching the petabyte scale, data related challenges such as formatting, management, and transfer are increasingly important topics which need to be addressed. The use of succinct data structures is one method of reducing physical size of a data set without the use of expensive compression techniques. In this work, we consider the use of 2- and 3-bit encoding schemes for genotype data. We compare the computational performance of allele or genotype counting algorithms utilizing genotype data encoded in both schemes.

Persistent Homology (PH) is a method of Topological Data Analysis that characterizes the topological structure of a space. Unfortunately, the computation of PH for high-dimensional and big data is not possible due to the exponential growth of the constructed complex. Fortunately, sparsification techniques can substantially reduce the size of the complex. This paper examines a sparsification technique ($\beta$-Sparsification) that produces a complex reduction capability that is scalable to a user-specified value $\beta$. At $\beta =0$ this scaling generates complexes that can have the same 1-Skeleton as the Vietoris–Rips complex; $\beta =1$ produces a Delaunay complex, and other values of $\beta$ produce a range of (unnamed) complexes. Experiments with $\beta$-Sparsification reveal that the topology of the sparsified simplicial complex is preserved for $0\le \beta \le 1$; for $\beta >1$, the complex begins to lose (potentially insignificant) topological features.

This paper presents a new scheduling mechanism to choose and process the next input event from the event-set of simulation objects in a logical process (LP). Events are prioritized based on a simulation object's working set. Working set of a simulation object is analogous to working set defined in virtual memory, and consists of input and output events referenced in the recent past (without time-faults). The simulation kernel exploits the causality framework to determine the working set size of a simulation object. In addition, the scheduler favors events that are within the estimated working set size. This working set based scheduling mechanism shows a performance improvement in the order or 10%-15%. This technique also improves the overall efficiency and memory utilization