Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer &...
Transcript of Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer &...
![Page 1: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/1.jpg)
Subset SumTeam Cthulu
Tushar Iyer & Aziel Shaw
Rochester Institute of Technology
December 5th, 2018
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 1 / 24
![Page 2: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/2.jpg)
Outline
1 Overview
2 Sequential & Parallel Program SummarySequential ProgramParallel Program
3 Program ScalingStrong ScalingWeak Scaling
4 Future WorkFuture Work
5 ConclusionWhat We LearnedFinal RemarksQuestions
6 Citations
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 2 / 24
![Page 3: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/3.jpg)
Overview
• Is an NP-Complete problem.
• Given a set of numbers and a target sum, find a set that totals thattarget sum.
• Dynamic Programming algorithm achieves best results both forperformance and parallelization.
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 3 / 24
![Page 4: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/4.jpg)
Sequential Program
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 4 / 24
![Page 5: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/5.jpg)
Parallel Program
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 5 / 24
![Page 6: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/6.jpg)
Strong Scaling - Tabular DataProblem Sizes 1 & 2
Figure 1: No Subset Solution Figure 2: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 6 / 24
![Page 7: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/7.jpg)
Strong Scaling - Tabular DataProblem Sizes 3 & 4
Figure 3: No Subset Solution Figure 4: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 7 / 24
![Page 8: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/8.jpg)
Strong Scaling - Tabular DataProblem Size 5
Figure 5: No Subset Solution Figure 6: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 8 / 24
![Page 9: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/9.jpg)
Strong Scaling - Running Time Vs. Cores
Figure 7: No Subset Solution Figure 8: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 9 / 24
![Page 10: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/10.jpg)
Strong Scaling - Speedup Vs. Cores
Figure 9: No Subset Solution Figure 10: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 10 / 24
![Page 11: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/11.jpg)
Strong Scaling - Efficiency Vs. Cores
Figure 11: No Subset Solution Figure 12: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 11 / 24
![Page 12: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/12.jpg)
Strong Scaling - Thoughts
Strong Scaling Hypothesis• We scale better with larger problem sizes
• Overall, we scale better when we do not find a solution
• Diminishing returns is hit sooner on smaller sizes, likely due to thefact that we find a solution sooner
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 12 / 24
![Page 13: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/13.jpg)
Weak Scaling - Tabular DataProblem Sizes 1 & 2
Figure 13: No Subset Solution Figure 14: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 13 / 24
![Page 14: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/14.jpg)
Weak Scaling - Tabular DataProblem Sizes 3 & 4
Figure 15: No Subset Solution Figure 16: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 14 / 24
![Page 15: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/15.jpg)
Weak Scaling - Tabular DataProblem Size 5
Figure 17: No Subset Solution Figure 18: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 15 / 24
![Page 16: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/16.jpg)
Weak Scaling - Running Time Vs. Cores
Figure 19: No Subset Solution Figure 20: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 16 / 24
![Page 17: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/17.jpg)
Weak Scaling - Sizeup Vs. Cores
Figure 21: No Subset Solution Figure 22: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 17 / 24
![Page 18: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/18.jpg)
Weak Scaling - Efficiency Vs. Cores
Figure 23: No Subset Solution Figure 24: Subset Exists
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 18 / 24
![Page 19: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/19.jpg)
Weak Scaling - Thoughts
Weak Scaling Hypothesis• We do not weak scale very well
• As with Strong scaling our non-solution is better than when we find asolution
• Also, as with Strong Scaling, we get better performance with largersets
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 19 / 24
![Page 20: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/20.jpg)
Future Work
• Allow both positive and negative inputs
• Allow for multiple numeric data types
• Implement C/CUDA variation
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 20 / 24
![Page 21: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/21.jpg)
What We Learned
• Variations of the SubsetSum algorithm [Bok11] [RMGF14] [PM15]
• How to implement SubsetSum using the PJ2 library [Kam]
• More experience with using interface (Spec) objects
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 21 / 24
![Page 22: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/22.jpg)
Final Remarks
• From our tests it is apparent our initial thoughts were correct
I Scaling is non-idealI We believe we are seeing diminishing returnsI Time increases as the level of work increases
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 22 / 24
![Page 23: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/23.jpg)
Questions
Any Questions?
Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 23 / 24
![Page 24: Subset Sum - Team Cthuluark/654/team/1/presentation4.pdf · Subset Sum Team Cthulu Tushar Iyer & Aziel Shaw Rochester Institute of Technology December 5th, 2018 Tushar j Aziel (RIT)](https://reader033.fdocument.pub/reader033/viewer/2022053010/5f0df4db7e708231d43ce988/html5/thumbnails/24.jpg)
References
Saniyah S. Bokhari, Parallel solution of the subset-sum problem: Anempirical study, Ohio State University, 2011, Date Accessed:September 24, 2018URL: https://pdfs.semanticscholar.org/f3fc/b462b7366ab7d91febe5fb92113535ff63dd.pdf.
Alan Kaminsky, Parallel java 2 library.
Dushan Petkovski and Igor Mishkovski, Parallel implementation of themodified subset sum problem in opencl, ICT Innovations 2015, WebProceedings ISSN null (2015), 144–153, Date Accessed: October 3,2018URL: http://proceedings.ictinnovations.org/attachment/paper/395/parallel-implementation-of-the-modified-subset-sum-
problem-in-opencl.pdf.
Z. Ristovski, I. Mishkovski, S. Gramatikov, and S. Filiposka, Parallelimplementation of the modified subset sum problem in cuda, 923–926,Date Accessed: September 19, 2018URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7034556.Tushar | Aziel (RIT) Parallel Computing - Presentation Four December 5th, 2018 24 / 24