Discrete and computational geometry on the plane lattice

• Project/Area Number: 19500004
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Ibaraki University
• Principal Investigator: KANO Mikio Ibaraki University, 工学部, 教授 (20099823)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2007: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: 離散幾何 / 計算幾何 / 平面格子上の幾何 / 赤点と青点の幾何 / 平衡分割 / 平面格子 / 2種点集合 / 多画像視覚分散 / 幾何的マッチング / 図形の視覚分散 / 赤点と青点 / 2色点集合 / 2等分割直角形 / 準直角形

Research Abstract

平面格子上の一般の位置に置かれた赤点と青点をそれぞれ2等分割する直角形が存在することを示し、同時にこのような2等分割直角形を求めるO(n log n)時間アルゴリズムを提案した。また、3つの凸領域で赤点と青点をそれぞれ3等分割できることも示した。さらに、格子線上に複数個の点の配置を許した場合にも、赤点と青点を同時に2等分割する準直角形の存在とその求め方など関連するいくつかの結果を得た。

Research Products

• [Journal Article] Bisections of two sets of points in the plane lattice, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (2009)
  • Author(s): M.Uno, T. Kawano and M.Kano
  • Journal Title: 電子情報通信学会論文誌A Vol.E92-A Pages: 502-507
  • Peer Reviewed
• [Journal Article] Compatible Geometric Matchings Discrete and Computational Geometry (2009)
  • Author(s): B.M.Abrego, E.M.Arkin, S. Fernandez -Merchant, F. Hurtado, M. Kano, J.S.B. Mitchell, J. Urrutia
  • Journal Title: Vol.41 Pages: 77-95
  • Peer Reviewed
• [Journal Article] Bisections of two sets of points in the plane lattice (2009)
  • Author(s): Miyuki Uno, Tomoharu Kaw ano and Mikio Kano
  • Journal Title: IEICE Transactions on Fundamentals E92-A Pages: 502-507
  • NAID: 10026855721
  • Peer Reviewed
• [Journal Article] Compatible Geometric Matchings (2009)
  • Author(s): B. M. Abrego, E. M. Arkin, M. Kano, 他4名
  • Journal Title: Discrete and Computational Geometry 41 Pages: 77-95
  • Peer Reviewed
• [Journal Article] Path factors and cycle factors of cubic bipartite graphs (2008)
  • Author(s): M. Kano, C. Lee and K. Suzuki
  • Journal Title: The Discussiones Mathematicae Graph Theory Vol.28 Pages: 551-556
  • Peer Reviewed
• [Journal Article] Monochromatic and heterochromatic subgraphs in edge-colored graphs---a survey (2008)
  • Author(s): M. Kano and Xueliang Li
  • Journal Title: Graphs Combinatorics Vol.24 Pages: 237-263
  • Peer Reviewed
• [Journal Article] Encompassing colored planar crossing-free geometric graphs (2008)
  • Author(s): F. Hurtado, M. Kano, D. Rappaport, Cs. D. Toth
  • Journal Title: Computational Geometry : Theory and Applications Vol.39 Pages: 14-23
  • Peer Reviewed
• [Journal Article] Encompassing colored planar crossing-free geometric graphs (2008)
  • Author(s): F. Hurtado M. Kano, D. Raonanort. Cs. Toth
  • Journal Title: Compurational Geothetry : Theory and Applications 39 Pages: 14-23
  • Peer Reviewed
• [Journal Article] Path factors and cycle factors of cubic bipartite graph (2008)
  • Author(s): M. Kane, C. Lee and K. Suzuki
  • Journal Title: The Discussiones Mathematicae Graph Theory 28 Pages: 551-556
  • Peer Reviewed
• [Journal Article] Monochromatic and heterochromatic subgraphs in edge-colored graphs-asurvey (2008)
  • Author(s): M. Kano and Xueliang Li
  • Journal Title: Graphs and Combinatorics 24 Pages: 237-264
  • Peer Reviewed
• [Journal Article] Encompassing colored planar straight line graphs (2008)
  • Author(s): Ferran Hurtado,
  • Journal Title: Computational Geometry:Theory and Applications 39 Pages: 14-23
  • Peer Reviewed
• [Journal Article] cryptography schemes with dihedral group access structure for many images, Information Security Practice and Experience (2007)
  • Author(s): M. Uno and M. Kano
  • Journal Title: LNCS Vol.4464 Pages: 344-359
  • Peer Reviewed
• [Journal Article] A neighborhood condition for graphs to have[a,b]-factors III, Discrete Geometry, Combinatorics and Graph Theory (2007)
  • Author(s): M. Kano and H. Matsuda
  • Journal Title: LNCS Vol.4381 Pages: 70-78
  • Peer Reviewed
• [Journal Article] General balanced subdivision of two sets of points in the plane, Discrete Geometry, Combinatorics and Graph Theory (2007)
  • Author(s): M. Kano and M. Uno
  • Journal Title: LNCS Vol.4381 Pages: 79-87
  • Peer Reviewed
• [Journal Article] Spanning trees with leaf distance at least four (2007)
  • Author(s): A. Kaneko, M. Kano and K. Suzuki
  • Journal Title: Journal Graph Theory Vol.55 Pages: 83-90
  • Peer Reviewed
• [Journal Article] Structure Theorem and Algorithm on $(1,f)$-odd subgraphs (2007)
  • Author(s): M. Kano and G.Y. Katona
  • Journal Title: Discrete Mathematics Vol.307 Pages: 1404-1417
  • Peer Reviewed
• [Journal Article] General balanced subdivision of two sets of points in the plane (2007)
  • Author(s): Mikio Kano
  • Journal Title: LNCS(Discrete Geometry, Combinatorics and Graph Theory) 4381 Pages: 79-87
  • NAID: 110004075872
  • Peer Reviewed
• [Journal Article] Structure Thegrem and Algorithm on $(1,f)$-odd subgraphs (2007)
  • Author(s): Mikio Kano
  • Journal Title: Discrete Mathematics 307 Pages: 1404-1417
  • Peer Reviewed
• [Journal Article] A neighborhood condition for graphs to have [a,b]-factors III (2007)
  • Author(s): Mikio Kano
  • Journal Title: LNCS(Discrete Geometry, Combinatorics and Graph Theory) 4381 Pages: 70-78
  • Peer Reviewed
• [Journal Article] Spanning trees with leaf distance at least four (2007)
  • Author(s): A. Kaneko
  • Journal Title: Journal Graph Theory 55 Pages: 83-90
  • Peer Reviewed
• [Presentation] 多画像ラブカードゲーム組合せ論 (2009)
  • Author(s): 加納幹雄
  • Organizer: 離散幾何研究集会2009/TGT20+α
  • Place of Presentation: 沖縄県琉球大学
  • Year and Date: 2009-03-04
• [Presentation] 多画像ラブカードゲーム (2009)
  • Author(s): 加納幹雄
  • Organizer: 組合せ論・離散幾何研究集会2009/TGT20+α
  • Place of Presentation: 沖縄琉球大学
  • Year and Date: 2009-03-04
• [Presentation] Invited Talk, Spanning trees with at most k leaves, International Conference on Graph Theory and it's Applications (2008)
  • Author(s): M.Kano
  • Organizer: AMRITA University, Coimbatore
  • Place of Presentation: Tamil Nadu, INDIA
  • Year and Date: 2008-12-11
• [Presentation] Spanning tree with at most k leaves (Invited Talk) (2008)
  • Author(s): Mikio Kano
  • Organizer: International Conference on Graph Theory and it's-Applications
  • Place of Presentation: Amrita, Coinibatore, Tamil Nadu, India
  • Year and Date: 2008-12-11
• [Presentation] Visual Secret Sharing Schemes with Cyclic Access Structure for Many Images (2008)
  • Author(s): M. UNO and M. KANO
  • Organizer: The 11th International Conference on Information Security and Cryptology
  • Place of Presentation: Seoul, Korea
  • Year and Date: 2008-12-04
• [Presentation] Elementary graphs with respect to(1, f)-odd factor (2008)
  • Author(s): 加納幹雄
  • Organizer: 離散数学とその応用研究集会2008
  • Place of Presentation: 水戸市三の丸庁舎茨城大学インフォメーションセンター
  • Year and Date: 2008-08-22
• [Presentation] Elementary graphs with respect to (1, f)-odd factor (2008)
  • Author(s): 加納幹雄
  • Organizer: 離散数学とその応用研究集会2008
  • Place of Presentation: 水戸市三の丸庁舎茨城大学インフォメーションセンター
  • Year and Date: 2008-08-22
• [Presentation] Star-uniform graphs with minimum degree one (2008)
  • Author(s): 加納幹雄
  • Organizer: 純粋数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
  • Place of Presentation: 府中市電気通信大学
  • Year and Date: 2008-07-04
• [Presentation] Star-uniform graphs with minimum degree one (2008)
  • Author(s): 加納幹雄
  • Organizer: 純粋数学及び応用数学としての組合ぜ論・離散数学そしてそめ周辺ワナクショップ
  • Place of Presentation: 電気通信大学府中市
  • Year and Date: 2008-07-04
• [Presentation] Star-uniform Graphs (2008)
  • Author(s): M. Kano, Y. Wu and Q. Yu
  • Organizer: 21st Cumberland Conference on Graph Theory, Combinatorics and Computing
  • Place of Presentation: Nashville, TN, USA
  • Year and Date: 2008-05-15
• [Presentation] 平面三角格子上におけるベンド数の少ないグラフ描画 (2008)
  • Author(s): 樫村賢治、加納幹雄
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 東京都千代田区法政大学
  • Year and Date: 2008-01-23
• [Presentation] 平面格子上の2種点集合の平行分割問題 (2008)
  • Author(s): 宇野美由紀、加納幹雄
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 東京都千代田区法政大学
  • Year and Date: 2008-01-23
• [Presentation] Star Uniform Graphs (2007)
  • Author(s): 加納幹雄
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 滋賀県瀬田龍谷大学
  • Year and Date: 2007-12-18
• [Presentation] Star Uniform Graphs (2007)
  • Author(s): Mikio Kano
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学 瀬田学舎
  • Year and Date: 2007-12-18
• [Presentation] A Spanning tree with at most k leaves in a graph, 32nd Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (2007)
  • Author(s): M. Kano and Aung Kyaw
  • Organizer: University of Otago
  • Place of Presentation: Dunedin, New Zealand
  • Year and Date: 2007-12-06
• [Presentation] A Spanning tree with at most $k$ leaves in a graph (2007)
  • Author(s): Mikio Kano
  • Organizer: 32ACCMCC
  • Place of Presentation: Dunedin, New Zealand
  • Year and Date: 2007-12-06
• [Presentation] グラフの偶数出次数の向き付け問題 (2007)
  • Author(s): 加納幹雄
  • Organizer: 第19回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜市横浜国立大学みなとみらいキャンパス
  • Year and Date: 2007-11-15
• [Presentation] 木をアクセス構造にもつ多画像視覚型秘密分散法 (2007)
  • Author(s): 宇野美由紀, 加納幹雄
  • Organizer: 電子情報通信学会情報セキュリティ研究会
  • Place of Presentation: 東京都港区芝公園機械振興会館
  • Year and Date: 2007-09-07
• [Presentation] Balanced Subdivision of Two Sets of Points in the Plane Lattice (2007)
  • Author(s): M.Kano
  • Organizer: Kyoto International Conference on Computational Geometry and Graph Theory
  • Place of Presentation: Kyoto University, Kyoto
  • Year and Date: 2007-06-12
• [Presentation] Balanced Subdivision of Two Sets of Points in the Plane Lattice (2007)
  • Author(s): Mikio Kano
  • Organizer: KyotoCGGT 2007
  • Place of Presentation: 京都大学
  • Year and Date: 2007-06-12
• [Presentation] Balanced Subdivision of Two Sets of Points in the Plane Lattice (2007)
  • Author(s): M.Kano
  • Organizer: CanaDAM 2007 Invite talk of Minisymposia,Banff Conference Center
  • Place of Presentation: Alberta, Canada
  • Year and Date: 2007-05-29
• [Presentation] Balanced Subdivision of Two Sets of Points in the Plane Lattice (2007)
  • Author(s): Mikio Kano
  • Organizer: CanaDAM 2007
  • Place of Presentation: Banff Conference Center, Alberta, Canada
  • Year and Date: 2007-05-29
• [Presentation] サイクルをアクセス構造にもつ多画像視覚型秘密分散法 (2007)
  • Author(s): 宇野美由紀、加納幹雄
  • Organizer: 電子情報通信学会情報セキュリティ研究会
  • Place of Presentation: 東京都港区芝公園機械振興会館
  • Year and Date: 2007-05-18
• [Presentation] Even out degree orientation of a graph, Invited talk (2007)
  • Author(s): M.Kano
  • Organizer: The 5th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: Tohoku University, Sendai
  • Year and Date: 2007-04-05
• [Presentation] Even out degree orientation of a graph (2007)
  • Author(s): Mikio Kano
  • Organizer: The 5th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 東北大学
  • Year and Date: 2007-04-05
• [Remarks] D. Avis, A. Bondy, M.Kano and N. Katoh, Computational Geometry and Graph Theory-The Akiyama-Chvatal Festschrift, Springer, (2007)
• [Remarks] J. Akiyama, W.Y.C. Chen, M.Kano, X. Li, Q. Yu, Discrete Geometry, Combinatorics and Graph Theory, LNCS 4381, Springer(2007)
• [Remarks] H. Ito, M. Kano, N. Kato, Y. Uno, Computational Geometry and Graph Theory, LNCS 4535, Springer(2008)
• [Remarks]
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• [Remarks] 茨城大学研究者情報総覧
  • URL: http://info.ibaraki.ac.jp/scripts/websearch/index.htm