| Presentation | 2016-01-29 Maximality of the Algebraic Connectivity of Complete Multipartite Graphs and a 2-Switch-Based Method for Finding Algebraic Connectivity Locally Maximizing Graphs Takuro Fujihara, Norikazu Takahashi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | How to reach a consensus is an important problem for multiagent networks. In the most well-known consensus algorithm proposed by Olfati-Saber and Murray, the state value of each agent varies continuously depending on those of other agents and converges to the average of the initial state values of all agents. In addition, the convegence rate is determined by the algebraic connectivity of the grath representing the interaction between agents. In this study, we consider the problem of finding a graph that maximizes the algebraic connectivity under a given degree sequence. First, we prove that each complete multipartite graph has the highest algebraic connectivity among all graphs with the same degree sequence. Next, we derive a lower bound for the algebraic connectivities of graphs that are obtained from a complete multipartite graph by applying a 2-switch. Finally, we propose 2-switch-based local search algorithms for finding algebraic connectivity locally maximizing graphs and evaluate their effectiveness experimentally. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | multiagent network / algebraic connectivity / complete multipartite graph / 2-switch |
| Paper # | RCC2015-92 |
| Date of Issue | 2016-01-22 (RCC) |
| Conference Information | |
| Committee | RCC |
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| Conference Date | 2016/1/29(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kansai University Umekita Laboratory |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Reliable Communication and Control |
| Chair | Masaaki Katayama(Nagoya Univ.) |
| Vice Chair | Shinsuke Hara(Osaka City Univ.) / Ryu Miura(NICT) |
| Secretary | Shinsuke Hara(Kyoto Univ.) / Ryu Miura(Hokkaido Univ.) |
| Assistant | Koji Ishii(Kagawa Univ.) / Kentaro Kobayashi(Nagoya Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Reliable Communication and Control |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Maximality of the Algebraic Connectivity of Complete Multipartite Graphs and a 2-Switch-Based Method for Finding Algebraic Connectivity Locally Maximizing Graphs |
| Sub Title (in English) | |
| Keyword(1) | multiagent network |
| Keyword(2) | algebraic connectivity |
| Keyword(3) | complete multipartite graph |
| Keyword(4) | 2-switch |
| 1st Author's Name | Takuro Fujihara |
| 1st Author's Affiliation | Okayama University(Okayama Univ.) |
| 2nd Author's Name | Norikazu Takahashi |
| 2nd Author's Affiliation | Okayama University(Okayama Univ.) |
| Date | 2016-01-29 |
| Paper # | RCC2015-92 |
| Volume (vol) | vol.115 |
| Number (no) | RCC-442 |
| Page | pp.pp.31-36(RCC), |
| #Pages | 6 |
| Date of Issue | 2016-01-22 (RCC) |