Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Run Time of Persistent Homology Computation with GPU
  Parallelization   Persistent homology is a crucial invariant that is used in many areas to
understand data. The $O(N^4)$ run time is a hindrance to its use on most large
datasets. We give a parallelization method to utilize multi-core machines and
clusters. We implement the computation of the $0^{th}$ persistent homology with
OpenMP parallelization and observe a 1.75 fold performance increase by using 2
threads on a dual core machine. We also benchmark the computation using larger
numbers of threads and show that the thread computational overhead decreases
performance. With GPU parallelization, we analytically and empirically decrease
the run time scaling from $O(N^4)$ to $O(N^3)$ and even $O(N^2)$ where $N$ is
the number of data points, for a large enough GPU. Next, we analytically show
run time scaling $O(N)$ for an even larger GPU.

34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th