# Parallelism Strategies for Big Data Delayed Transfer Entropy Evaluation
## 5 Conclusions  
DTE is a probabilistic nonlinear measure to infer causality within a time delay between time-series. However, the DTE algorithm demands high processing power, requiring approaches to overcome such limitation. A distributed processing approach was presented to accelerate DTE computation using parallel programming over a heterogeneous low-cost computer cluster. In addition, Data and Task Parallelism strategies were compared to optimize software execution time.  
The main contribution of this study is exploring a low-cost Beowulf heterogeneous computer cluster as a new alternative to existent FPGA TE [36] or GPU DTE [37] implementations. The low-cost nature of Beowulf computer clusters and its simple setup enables using existing computers from research laboratories or universities, helping mitigate DTE performance issues without the acquisition of expensive hardware such as FPGAs or GPU cards. This is especially attractive to places where research funding lacks enough resources or where DTE usage is too infrequent to justify any purchases.  
Additionally, in order to verify cluster feasibility, using a Task Parallelism strategy to increase DTE algorithm performance in a heterogeneous cluster was shown as a faster alternative in comparison to Data Parallelism. Having in sight big data analysis importance, it is a significant result, since it will enable causal inference for bigger previous inapplicable datasets or with better causality statistical evidence.  
Having verified Task Parallelism as a better approach to DTE in a heterogeneous Beowulf cluster, it remains open how the number of computing nodes affects performance. Thus, future research  
Figure 5: DTE Task Parallelism performance comparison between different computing nodes to highlight cluster heterogeneity. In Task Parallelism, each experiment spawned _number of channels_\(*\) (_number of channels_\(-1\)) DTE tasks of the same size across computing nodes, their execution times were used to calculate quickening of the \(y\)-axis computing node over the \(x\)-axis computing node and finally an average of calculated speedups for each cell was made. An execution log used to generate this plot was from 20 surrogates. Values are given in relative quickening.  
should investigate how scalable Task Parallelism is after an increased number of computing nodes observing [PERSON]'s law [89]. Along the same lines, performance, scalability and cost analysis of renting Cloud Computing nodes to build a cluster on demand to explore causality in big data using DTE is needed.  
Studying DTE applied to Big Data demands high processing power, for example, to increase confidence from 95.24% (\(n\) = 20) to 99.9% (\(n\) = 999), Task Parallelism run time is increased from 0.9 days to estimated 45.27 days using our setup and data. Although a long runtime is a notorious improvement from about half a year from extrapolated Data Parallelism run time. This highlights the importance of hardware performance to increase statistical confidence and gives strong support to keep researching quicker methods for DTE.  
One open question unique to our cluster configuration is if the RAM amount has a correlation with performance in computing nodes when executing Task Parallelism as suggested by our results. Moreover, different parallelism strategies can be tested on a case by case basis aiming to accelerate processing of the ever increasing data size.  
Conceptualization, J.R.D.; Funding acquisition, J.R.D. and C.D.M.; Investigation, J.R.D. and J.N.d.O.J.; Methodology, [PERSON]; Resources, C.D.M.; Software, C.D.M.; Supervision, C.D.M.; Writing--original draft, J.R.D. and J.N.d.O.J.; Writing--review & editing, J.N.d.O.J.  
This research was partially funded by **CNPq**-Project 465755/2014-3; **FAPESP** Project 2014/50851-0; **BPE Fapesp** 2018/19150-6.  
The authors would like to thank previous people who worked on source code of the previous version.  
The authors declare no conflict of interest.