2022 Fiscal Year Final Research Report
Advanced algorithm and its applications for the domination problem in complex networks
Project/Area Number |
18K11182
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 60020:Mathematical informatics-related
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Research Institution | Kyoto University |
Principal Investigator |
ZHAO LIANG 京都大学, 総合生存学館, 准教授 (90344902)
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Project Period (FY) |
2018-04-01 – 2023-03-31
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Keywords | 複雑ネットワーク / 支配集合 / 代表集合 / アロメトリー / 一票の格差 |
Outline of Final Research Achievements |
The purposes of this research are to show (1) an allometry phenomenon between the size of a minimum distance-k dominating (or representative) set and the size of the complex network; (2) a theoretical model explaining that phenomenon; and (3) applications of that phenomenon in real problems. For (1), a phenomenon D ∝ a-th power of A for the size D of an appropriate distance-k dominating set and the size A of the network has been confirmed for various complex networks (a<1 is a constant). For (2), with some reasonable assumptions, a theoretical model to explain the above allometry phenomenon for social networks has been given. And for (3), with the allometry phenomenon for social networks, it is suggested that, to study a malapportionment problem, the average weight of an individual (or a vote) shall be calculated according to the given allometry, not by just dividing the number of seats by the population (or votes).
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Free Research Field |
数理情報学
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Academic Significance and Societal Importance of the Research Achievements |
権利についての平等は基本的な人権の一つである(世界人権宣言第一条)。国会や議会においては、民衆が平等に代表されなければならない。その状況は、人類社会の数世紀の努力によって、人種や性別などによる差別が廃止され、大きく進展してきたと言えよう。本研究は、さらに一歩進んで、これまで採用されてきた比例代表の考え方、すなわち「議席数÷人口」で一人当たりの代表される度合いを求めてその値を同一しようとする方法は、間違って計算している可能性が高いことを数理的に示した。この成果は、ネットワーク構造の分析という学術的意義と、代表の平等という重要な社会課題を考える際の方法論を与える。
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