2022 Fiscal Year Research-status Report
Towards a theory of smoothed analysis for distributed computing
| Project/Area Number |
21K17703
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| Research Institution | Japan Advanced Institute of Science and Technology |
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Principal Investigator |
シュワルツマン グレゴリー 北陸先端科学技術大学院大学, 先端科学技術研究科, 准教授 (20815261)
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | Smoothed analysis / Graph algorithms |
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| Outline of Annual Research Achievements |
In the past year I have been working with collaborators in Europe and Israel on considering the smoothed complexity of online algorithms. We have some preliminary results for general covering problems which we want to formalize and submit for publication.
I've also published a single author paper in ICLR, a leading machine learning conference. The paper considers the fundamental problem of mini-batch k-means. While the current analysis is worst-case, the analysis draws inspiration from smoothed analysis techniques.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The project is progressing well, with the current focus being applying smoothed analysis to online algorithms. This will be, to the best of my knowledge, the first use of smoothed analysis in this field. We have some intermediate results for the fractional set cover problem, and we aim to extend them to the integral case.
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| Strategy for Future Research Activity |
This year we plan to complete our results for the integral case of online set cover and publish the results in a leading conference. We then aim to generalize our results to general covering problems. It would also be of interest to extend our results to the distributed setting.
I also wish to consider the smoothed complexity of mini-batch k-means. This was the motivation for the ICLR paper, and I still believe better results can be achieved in this case.
To achieve the above I plan to meet collaborators from Israel and Europe, and attend international conferences.
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| Causes of Carryover |
Although we achieved promising preliminary results, an additional year is needee to achieve the full potential of these results. This means writing a complete writeup, considering additional models (e.g., distributed) and submitting to a top conference.
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