2022 Fiscal Year Final Research Report
Analysis of consensus times for non-linear opinion dynamics
| Project/Area Number |
19K20214
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60010:Theory of informatics-related
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| Research Institution | Chuo University (2019-2020, 2022)
Tokyo Institute of Technology (2021) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | 分散投票モデル / マルコフ連鎖 |
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| Outline of Final Research Achievements |
We study a simple probabilistic model called 2-choices dynamics (2-CHOICES). While the differences between the model and existing models are slight, 2-CHOICES shows rapid convergence to a single opinion on specific graph structures, making it desirable for basic distributed computation. However, little is known about its behaviour on general graph structures.
We showed the existence of a phase transition in convergence time on graphs representing community structures (stochastic block model) and provided an example where exponential time is required for convergence. We also characterised the requirements for opinion update rules that allow fast convergence from a majority voting perspective and presented logarithmic consensus time on expander graphs.
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| Free Research Field |
アルゴリズム理論
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| Academic Significance and Societal Importance of the Research Achievements |
単純, 局所的なルールに基づくシステムはその理解, 利用のし易さに留まらず, 管理・保全を含めた多くの柔軟性を包含する. 単純性というある意味で“制限された”環境下におけるシステムがどの程度の計算能力を持つかという問いは, 理論的にも所望の問題に対して必要な資源を明確にするという意味で需要が大きい. 本研究で明らかになった2-CHOICESを含めた局所的な更新規則とその威力は既存研究を大きく一般化するものであり, 得られた解析技法は研究対象となったルールに留まらず, ランダムウォークを始めとした他の有用な確率モデルへも適用されつつあり, その意義は大きいと言える.
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