New Efficient Approach to Solve Big Data Systems Using Parallel Gauss–Seidel Algorithms

Round 1

Reviewer 1 Report

The research work presented in this paper is titled “New Efficient Approach to Solve Big Data Systems Using Parallel Gauss-Seidel Algorithms”. The work seems novel and has the potential for impact to the discipline. However, the paper needs major improvement. The authors are suggested to make the necessary changes/updates to their paper as per the following comments:

1. The introduction section needs improvement: Please highlight the challenges that exist in the previous works that have been reviewed to support the relevance of doing this research work
2. For the time complexity analysis presented in Section 5.1 – what are the best-case and worst-case scenarios? What are the respective conditions for the best case and worst case?
3. Please elaborate why it is important to validate the algorithms on real-world data on wine quality and bike rental and not on data from any other application domains?
4. The authors state – “Data-generating sources include internet of things (IoT), social websites, smart-devices, sensor networks, digital images/videos, multimedia signal archives for surveillance, business-activity records, web logs, health (medical) records, on-line libraries, eCommerce, scientific research projects, smart cities, and so on.” – While this is true but references should be provided for each of these examples (data generating sources) to support this claim. Cite this recent paper - https://doi.org/10.3390/info12020081 related to sensor networks and smart devices. Similarly, cite other recent papers to support the other examples.
5. Discussion of results needs improvement: Please compare the results (both quantitatively and qualitatively) with prior works in this field to discuss how it outperforms all the prior works that have been reviewed at the beginning of the paper.
6. The limitations of the study should be clearly mentioned as well as the scope for future work should be outlined.

Author Response

Thank you very much for your kind help, precious guidance, and outstanding review work for the above-referenced manuscript. Please forward our sincerest gratefulness to the associate editor and both reviewers, who helped us with invaluable comments to improve the quality of this research. As per your kind request, we have revised the manuscript thoroughly according to the reviewers' precious advice and provide the point-to-point responses to address all invaluable questions and comments from the reviewers as follows:

1. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We have revised this draft introduction section to highlight the challenges that exist in the previous works and how this research overcome these difficulties.
2. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We have added a paragraph of a discussion in Sec. 5.1.
3. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. There are no restrictions about what datasets to be used. Actually, any dataset used to solve a system of linear equations can be applied by our proposed methods investigated in this work.
4. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We have added references to support this claim.
5. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We have provided further numerical results to compare run time of the proposed methods with related methods in Sec. 6.3.
6. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. The limitations of the proposed GS methods and future works are provided at Conclusion section.

Reviewer 2 Report

According to this referee, the paper titled “New Efficient Approach to Solve Big Data Systems Using Parallel Gauss-Seidel Algorithms" fit the objectives of the MDPI Section Mathematics.

According to this referee:

• The considered topic is interesting and up to date.
• The general organization of the paper is acceptable.
• The title of the paper is well chosen.
• The abstract is adequate.
• The writing is clear.
• Enough important references (46) are included in the References section and all references that are listed in the bibliography are referenced in the text.
• The quality of English is acceptable for non-native English speaking authors.
• The paper is of a right length.

The presentation is clear.

Remarks and suggestions:

The lines started after the formulas is better to start from the first position of the line. Mostly, these are lines started with "where" but not only.

Author Response

The lines started after the formulas is better to start from the first position of the line. Mostly, these are lines started with "where" but not only.

We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We have revised these formated accordinly. 

Reviewer 3 Report

The paper starts with the assumption "once a large matrix can be processed with its factorized form" which describes one criticism on the paper. Afterwards the paper look mathematically correct without proving the announced results ("for large systems") in the numerical evaluation.

Critical remarks:

• line 48 and §6: What are the costs (in run time) for the low-rank factorization V=WH in comparison to the solving algorithm in the paper.
• §6: No run times are presented for the studies. Time complexity is not run time and parallelization results with run time are a hoax.
• No run time is presented for the factorization of V=WH.
• No run time is presented for solving the system with the original matrix V.
• Fig. 7: Even a matrix V of dimension 2500x2000 is not large. , i.e. there is no benefit in using the proposed algorithm taking into account the highly optimized Lapack or mkl libraries. The reviewer is in doubt whether the presented algorithm (including and excluding factorization!) is faster than simply solve the original system via mkl library calls.
• The authors have to present results for m,n in the range of  10^4, 10^5 (approx. 100 GB) and they have to check whether there is a break-even-point or not  comparing their GS with the library calls regarding run time.

The paper is useless without the requested run time comparisons above.

Author Response

Thank you very much for your kind help, precious guidance, and outstanding review work for the above-referenced manuscript. Please forward our sincerest gratefulness to the associate editor and both reviewers, who helped us with invaluable comments to improve the quality of this research. As per your kind request, we have revised the manuscript thoroughly according to the reviewers' precious advice and provide the point-to-point responses to address all invaluable questions and comments from the reviewers as follows:

1. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We add run time complexity numerical results for the factorization of V=WH in Sec. 6.
2. We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice. We also add run time complexity for solving the matrix V with respect to different dimensions in Sec. 6 and compare the proposed GSA with Lapack software package.

Round 2

Reviewer 1 Report

The authors have significantly updated the paper as per all my comments and suggestions. I do not have any additional comments at this point. I recommend the publication of the paper in its current form. 

Author Response

We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice.

Reviewer 3 Report

All requests have been considered.

Author Response

We are very grateful to the associate editor for his/her profound knowledge, keen insight, excellent viewpoint, and precious advice.