2021 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 – 2023-03-31
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| Keywords | Smoothed analysis / Distributed computing |
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| Outline of Annual Research Achievements |
In the 2021 fiscal year I have co-authored 3 papers which appeared in top tier conferences in the field of distributed computing (SPAA, DISC). These papers deal with dynamic networks and smoothed analysis. We show that using smoothed analysis we are able to overcome the impossibility results for the fundamental problem of load balancing. This brings us one step closer towards a theoretic complexity model which truly captures the hardness of this fundamental problem. We also applied smoothed analysis to the field of population protocols. Again, we show that the worst case lower bounds are fragile, and if there is even the tiniest amount of noise in the system we are able to achieve fast algorithms for the fundamental problem of leader election. Finally, we also present new algorithms for detecting subgraphs in highly dynamic networks. Are algorithms are fast, simple, and have a constant amortized running time.
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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
We have managed to apply smoothed analysis to fundamental problems in the distributed setting. Specifically, load balancing in dynamic networks and leader election in population protocols. This shows the applicability of smoothed analysis for distributed dynamic systems.
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| Strategy for Future Research Activity |
We plan to consider more fundamental problems in these models. Specifically, we believe that we can solve an even more difficult variant of load balancing using our techniques. We also believe that we can develop faster population protocols for leader election and further problems.
Furthermore, we believe that smoothed analysis might be useful for analyzing real world networks. Often, worst-case analysis does not capture the true hardness of real world systems. We believe that it might be possible to consider fundamental problems in data-centers (i.e, P4 networks), and show that smoothed analysis can explain the performance of algorithms in these systems. One promising candidate problem is the problem of computing a shallowest BFS tree. This is a fundamental task in this environment, however it appears that we cannot get a solution better than a 2-approximation. On the other hand it appears that heuristic solutions work extremely well in practice. We would like to bridge this gap by considering the smoothed complexity of this problem
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| Causes of Carryover |
Due to the covid pandemic it was impossible to travel internationally and invite research collaborators. This years the travel restrictions have been relaxed and I plan to use the funds as stated in the original proposal.
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