Approximation algorithms for set cover problems with graph structures

• Project/Area Number: 25330026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Kyoto University
• Principal Investigator: ZHAO LIANG 京都大学, 総合生存学館, 准教授 (90344902)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 支配集合 / 集合被覆 / distance dominating / network algorithm / democratic number / outerplanar graph / 一票の格差 / Dominating set / distacne dominating / set cover / distance covering

Outline of Final Research Achievements

Given a graph, let us define the domination area of a vertex v by the set of vertexes within distance k from v. This research considers to find a minimum set of vertexes that dominates all or specified ratio of vertexes. For a k>=2 and large scale networks, based on the idea to improve by utilizing the graph structure, this study designed some new linear-time algorithms for some classes of graphs. Empirical results show that proposed methods improve from previous studies. Finally, the algorithms are applied to some social problems as well.

Research Products

• [Int'l Joint Research] 重慶大学(中国)
• [Int'l Joint Research] 大連理工大学(中国)
• [Journal Article] $\gamma_k(n) = \max \{\lfloor n/(2k+1) \rfloor, 1\}$ for maximal outerplanar graphs with $n \bmod (2k+1) \le 6$ (2017)
  • Author(s): Liang Zhao
  • Journal Title: Journal of Information Processing Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimal assignment of wide-area evacuation centers for Kyoto city (2017)
  • Author(s): Liang Zhao, Tetsuya Hashitani, Yukako Takeshita, Riku Hayami, Yukiko Ninomiya, Kengo Umegagi, Daichi Azuma, Ryota Miyamoto, Tomomi Itani
  • Journal Title: Proc. 5th Operations Research and Statistics Volume: 1 Pages: 171-174
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Majority Dominating and Democratic Number: A Proposal to Define the Democracy of a Social Network (2016)
  • Author(s): Liang Zhao
  • Journal Title: Proc. 4th Annual International Conference on Operations Research and Statistics Volume: 1 Pages: 66-67
  • DOI: 10.5176/2251-1938_ors16.19
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] $gamma_k(G) le lfloor frac{n}{2k+1} rfloor$ for maximal outerplanar graphs satisfying $n bmod (2k+1) le 4$ (2014)
  • Author(s): Liang Zhao, Jia Li and Dorothea Wagner
  • Journal Title: Proc. of the 17th Korea-Japan Joint Workshop on Algorithms and Computation (WAAC 2014) Volume: 1
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A note on distance dominating in maximal outerplanar graphs (2014)
  • Author(s): Liang Zhao, Jia Li, Dorothea Wagner
  • Journal Title: 情報処理学会 研究報告アルゴリズム（AL） Volume: 2014-AL-147 Pages: 1-3
• [Journal Article] An Improved Linear-Time Algorithm for Finding Small L-VertexCovers (2013)
  • Author(s): Liang Zhao, Hiroshi Kadowaki
  • Journal Title: Proc. 16th Korea-Japan Joint Workshop on Algorithms and Computation Volume: 1 Pages: 38-42
  • Peer Reviewed
• [Journal Article] A Practical Approach for Finding Small {Independent, Distance} Dominating Sets in Large-Scale Graphs (2013)
  • Author(s): Liang Zhao, Hiroshi Kadowaki, Dorothea Wagner
  • Journal Title: Lecture Notes in Computer Science Volume: 8266 Pages: 157-164
  • DOI: 10.1007/978-3-319-03889-6_18
  • ISBN: 9783319038889, 9783319038896
  • Peer Reviewed
• [Presentation] A Note on Distance Domination in Maximal Outerplanar Graphs (Extended Abstract) (2016)
  • Author(s): Liang Zhao
  • Organizer: 19th Japan Conference on Discrete and Computational Geometry, Graphs, and Games
  • Place of Presentation: Tokyo Univ. of Science, Tokyo, Japan
  • Year and Date: 2016-09-02
  • Int'l Joint Research
• [Presentation] 民主度指数を用いた代表選と一票格差への考察 (2016)
  • Author(s): 趙 亮
  • Organizer: 情報処理学会第13回ネットワーク生態学シンポジウム
  • Place of Presentation: 千葉木更津オークラアカデミアパークホテル
  • Year and Date: 2016-08-22
• [Presentation] ネットワークで見る独裁と民主の差 (2015)
  • Author(s): 趙 亮
  • Organizer: 京都大学アカデミックデイ2015
  • Place of Presentation: 京都大学
  • Year and Date: 2015-10-04
• [Book] "Finding Small Dominating Sets in Large-Scale Networks," in Big Data of Complex Networks (2016)
  • Author(s): Liang Zhao
  • Publisher: Chapman and Hall/CRC
• [Remarks] ネットワークで見る独裁と民主の差
  • URL: http://research.kyoto-u.ac.jp/academic-day/2015/26/