Construction of Geometric Data Processing Optimization Theory by Using Global Norms

2009 Fiscal Year Final Research Report

• Project/Area Number: 18300001
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Tohoku University
• Principal Investigator: TOKUYAMA Takeshi Tohoku University, 大学院・情報科学研究科, 教授 (40312631)
• Co-Investigator(Kenkyū-buntansha): CHUN Jinhee 東北大学, 大学院・情報科学研究科, 准教授 (80431550)
• Co-Investigator(Renkei-kenkyūsha): ASANO Tetsuo 北陸先端科学技術大学院大学, 情報科学研究科, 教授 (90113133)
• Project Period (FY): 2006 – 2009
• Keywords: アルゴリズム / 数理工学 / 幾何学 / 情報システム

Research Abstract

We have established novel theory of geometric data processing based on optimization using global norms. We have given optimal compression of geometric objects and optimal approximation of visual images with respect to global norms. Moreover, we proposed new concept of discrete Euclidean axioms on a grid, and gave a novelconstruction of a family of digital segments together with its theoretical optimality. We have published our results in 31 refereed journal/conference papers, and given 36 international/domestic conference presentations. We also did educational campaign via three textbooks and a TV interview.

Research Products

• [Journal Article] Distance Trisector of a Segment and a Point (2010)
  • Author(s): Jinhee Chun, Yuji Okada, Takeshi Tokuyama
  • Journal Title: Interdisciplinary Information Sciences Vol. 16, No. 1 Pages: 119-126
  • Peer Reviewed
• [Journal Article] 高密度部分グラフの抽出 (2009)
  • Author(s): 徳山豪
  • Journal Title: 電子情報通信学会誌 2009-2 Pages: 82-89
  • Peer Reviewed
• [Journal Article] All Farthest Neighbors in the Presence of Highways and Obstacles (2009)
  • Author(s): Sang Won Bae, Matias Korman, Takeshi Tokuyama
  • Journal Title: Proc.WALCOM 2009, Springer LNCS 5431 Pages: 71-82
  • Peer Reviewed
• [Journal Article] "Distance k-Sectors and Zone Diagra" ms (2009)
  • Author(s): Keiko Imai, Akitoshi Kawamura, Jiri Matousek, Yu Muramatsu, Takeshi Tokuyama
  • Journal Title: Abstracts of EuroCG 2009 Pages: 191-194
  • Peer Reviewed
• [Journal Article] Algorithms for Computing the Maximum Weight Region Decomposable into Elementary Shapes (2009)
  • Author(s): Jinhee Chun, Ryosei Kasai, Matias Korman, Takeshi Tokuyama
  • Journal Title: Proceedings of the 20th Annual International Symposium on Algorithms and Computation (ISAAC' 09), LNCS 5878 Pages: 1166-1174
  • Peer Reviewed
• [Journal Article] Algorithms for Optimal Segmentation of Regions Decomposable into Basic Shapes (2009)
  • Author(s): Jinhee Chun, Ryosei Kasai, Matias Korman, Takeshi Tokuyama
  • Journal Title: Proceedings of the 11th Japan-Korea Joint Workshop on Algorithms and Computation (WAAC' 09) Pages: 138-145
  • Peer Reviewed
• [Journal Article] Consistent digital rays (2009)
  • Author(s): Jinhee Chun, Matias Korman, Martin Nollenburg , Takeshi Tokuyama
  • Journal Title: Discrete and Computational Geometry Vol. 42, No. 3 Pages: 359-378
  • Peer Reviewed
• [Journal Article] All Farthest Neighbors in the Presence of Highways and Obstacles (2009)
  • Author(s): Sang Won Bae, Matias Korman, Takeshi Tokuyama
  • Journal Title: WALCOM 2009 Pages: 71-82
  • Peer Reviewed
• [Journal Article] Directional Geometric Routing on Mobile Ad Hoc Networks (2009)
  • Author(s): Kazushige Sato, Takeshi Tokuyama
  • Journal Title: COCOON 2009 Pages: 527-537
  • Peer Reviewed
• [Journal Article] Consistent digital rays (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Nollenburg, Takeshi Tokuyama
  • Journal Title: Proceedings of the 24th European Workshop on Computational Geometry (EuroCG'08) Pages: 169-172
  • Peer Reviewed
• [Journal Article] Consistent digital rays (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Nollenburg, Takeshi Tokuyama
  • Journal Title: Proceedings of the Twenty-Fourth Annual Symposium on Computational Geometry (SoCG' 08) Pages: 355-364
  • Peer Reviewed
• [Journal Article] Finding the maximum union of closures is NP-hard, even for trees (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Nollenburg, Takeshi Tokuyama
  • Journal Title: Proceedings of the 11th Japan-Korea Joint Workshop on Algorithms and Computation (WAAC' 08) Pages: 139-144
  • Peer Reviewed
• [Journal Article] Optimal Insertion of a Segment Highway in a City Metric (2008)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Journal Title: Proceedings of the 14th international conference on Computing and Combinatorics (COCOON' 08), LNCS Pages: 611-620
  • Peer Reviewed
• [Journal Article] Optimal Insertion of a Segment Highway in a City Metric (2008)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Journal Title: Proceedings of COCOON 2008, Springer LNCS 5092 Pages: 611-620
  • Peer Reviewed
• [Journal Article] Minimizing interference of a wireless ad-hoc network in a plane (2008)
  • Author(s): Magnus M, Halldorsson, Takeshi Tokuyama
  • Journal Title: Theor, Comput, Sci 402(1) Pages: 29-42
  • Peer Reviewed
• [Journal Article] Dense subgraph problems with output-density conditions (2008)
  • Author(s): Akiko Suzuki, Takeshi Tokuyama
  • Journal Title: ACM Transactions on Algorithms 4(4) Pages: 1-18
  • Peer Reviewed
• [Journal Article] Geometric Problems on Ad-Hoc Network Design (2008)
  • Author(s): Takeshi Tokuyama
  • Journal Title: RIMS Workshop on Discrete Mathematics and Computational Geometry Pages: 135-143
  • Peer Reviewed
• [Journal Article] Distance Trisector of Segments and Zone Diagram of Segments in a Plane (2007)
  • Author(s): Jinhee Chun, Yuji Okada, Takeshi Tokuyama
  • Journal Title: Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD' 07) Pages: 66-73
  • Peer Reviewed
• [Journal Article] Voronoi Diagram with Respect to Criteria on Vision Information (2007)
  • Author(s): Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama
  • Journal Title: 4^<th> Symposium on Voronoi diagram (IEEE Press) Pages: 25-32
  • Peer Reviewed
• [Journal Article] Fixed-Parameter Tractability for Non-Crossing Spanning Trees (2007)
  • Author(s): Magnus M, Halldorsson, Christian Knauer, Andreas Spillner, Takeshi Tokuyama
  • Journal Title: 10^<th> Workshop on Data Structures and Algorithms, LNCS 4619 Pages: 412-420
  • Peer Reviewed
• [Journal Article] Zone diagrams, existence, uniqueness and algorithmic challenge (2007)
  • Author(s): Tetsuo Asano, Jiri Matousek, Takeshi Tokuyama
  • Journal Title: 18^<th> ACM-SIAM Symposium on Discrete Algorithms (SODA 2007) Pages: 756-765
  • Peer Reviewed
• [Journal Article] Zone diagrams, existence, uniqueness and algorithmic challenge (2007)
  • Author(s): Tetsuo Asano, Jiri Matousek, Takeshi Tokuyama
  • Journal Title: SIAM Journal on Computing 37-4 Pages: 1182-1198
  • Peer Reviewed
• [Journal Article] Recent progress on combinatorics and algorithms for low discrepancy roundings (2007)
  • Author(s): Takeshi Tokuyama
  • Journal Title: Graphs Combin 23, supp.1, 1 Pages: 359-378
  • Peer Reviewed
• [Journal Article] The distance trisector curve (2007)
  • Author(s): Tetsuo Asano, Jiri Matousek, Takeshi Tokuyama
  • Journal Title: Adv, Math 212, no, 1 Pages: 338-360
  • Peer Reviewed
• [Journal Article] Linear Time Algorithm for Approximating a Curve by a Single-peaked Curve (2006)
  • Author(s): Jinhee Chun, Kunihiko Sadakane, Takeshi Tokuyama
  • Journal Title: Algorithmica Vol. 44, No. 2 Pages: 103-115
  • Peer Reviewed
• [Journal Article] Efficient Algorithms for Constructing a Pyramid from a Terrain (2006)
  • Author(s): Jinhee Chun, Kunihiko Sadakane, Takeshi Tokuyama
  • Journal Title: IEICE Transactions Vol. E89-D, No. 2 Pages: 783-788
  • Peer Reviewed
• [Journal Article] 関数近似における幾何学アルゴリズムの最近の進展, データ解析への応用に向けて (2006)
  • Author(s): 徳山豪
  • Journal Title: 電子情報通信学会論文誌A J89-A-6 Pages: 419-429
  • Peer Reviewed
• [Journal Article] Minimizing Interference of a Wireless Ad-Hoc Network in a Plane (2006)
  • Author(s): Magnus M, Halldorsson, Takeshi Tokuyama
  • Journal Title: Proc, ALGOSENSOR 2006, Springer LNCS 4240 Pages: 71-82
  • Peer Reviewed
• [Journal Article] Efficiently pricing European Asian options- ultimate implementation and analysis of the AMO algorithm (2006)
  • Author(s): Akiyoshi Shioura, Takeshi Tokuyama
  • Journal Title: Information Processing Letters 100 2006 Pages: 213-219
  • Peer Reviewed
• [Journal Article] Polyline "Fitting of Planar Points under Min-sum Criteria" (2006)
  • Author(s): Boris Aronov, Tetsuo Asano, Naoki Katoh, Kurt Mehlhorn, Takeshi Tokuyama
  • Journal Title: Int, J, Comput, Geometry App.1 16(2-3) Pages: 97-116
  • Peer Reviewed
• [Journal Article] The Distance Trisector Curve (2006)
  • Author(s): Tetsuo Asano, Jiri Matousek, Takeshi Tokuyama
  • Journal Title: Proceedings of the 38th ACM Symposium on Theory of Computing (STOC06) Pages: 336-343
  • Peer Reviewed
• [Presentation] Deterministic Constant Work Space Algorithms for 2-D Linear Programming (2010)
  • Author(s): Testuo Asano, Danny Chen, Takeshi Tokuyama
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 東京
  • Year and Date: 2010-03-12
• [Presentation] センサーネットワークの位相情報の検知に関する研究 (2010)
  • Author(s): 成田龍太, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 東京
  • Year and Date: 2010-03-12
• [Presentation] 画像切り出しに対するアルゴリズムの提案 (2010)
  • Author(s): 安齋進也, 全眞嬉, 葛西亮生, コルマンマティアス, 徳山豪
  • Organizer: 冬のLAシンポジウム
  • Place of Presentation: 京都
  • Year and Date: 2010-02-02
• [Presentation] イルジマトウシェク, ユークリッド空間及びノルム空間における地帯図 (2010)
  • Author(s): 河村彰星, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 福岡
  • Year and Date: 2010-01-25
• [Presentation] イルジマトウシェク, ダニエルレエム, 距離等分の存在 (2010)
  • Author(s): 今井桂子, 河村彰星, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 福岡
  • Year and Date: 2010-01-12
• [Presentation] 複数のデジタル図形の最適切り出しについて (2009)
  • Author(s): 全眞嬉, 葛西亮生, コルマンマティアス, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 仙台
  • Year and Date: 2009-10-16
• [Presentation] 基単調領域の非交差和領域の最適イメージ切り出しアルゴリズム (2009)
  • Author(s): 全眞嬉, 葛西亮生, コルマンマティアス, 徳山豪
  • Organizer: 第8回FIT情報科学技術フォーラム2009
  • Place of Presentation: 仙台
  • Year and Date: 2009-09-02
• [Presentation] ジャストインタイムウェブ広告におけるタクソノミ自動生成手法 (2009)
  • Author(s): 櫻庭敦之, 成田龍太, 全眞嬉, 徳山豪
  • Organizer: 第8回FIT情報科学技術フォーラム2009
  • Place of Presentation: 仙台
  • Year and Date: 2009-09-02
• [Presentation] 基本図形に分割可能な領域の最適切り出しアルゴリズム (2009)
  • Author(s): 葛西亮生, コルマンマティアス, 全眞嬉, 徳山豪
  • Organizer: LAシンポジウム2009
  • Place of Presentation: 松島
  • Year and Date: 2009-07-22
• [Presentation] ジャストインタイムウェブ広告におけるタクソノミ自動生成手法 (2009)
  • Author(s): 櫻庭敦之, 成田龍太, 全眞嬉, 徳山豪
  • Organizer: LAシンポジウム2009
  • Place of Presentation: 松島
  • Year and Date: 2009-07-22
• [Presentation] Algorithms for optimal segmentation of regions decomposable into basic shapes (2009)
  • Author(s): Ryosei Kasai, Jinhee Chun, Matias Korman, Takeshi Tokuyama
  • Organizer: コンピューテション研究会, IEICE Technical Report
  • Place of Presentation: 北海道
  • Year and Date: 2009-06-29
• [Presentation] 基本図形分割可能領域の最適切り出しアルゴリズム (2009)
  • Author(s): 葛西亮生, 全眞嬉, マティアスコルマン, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 北海道
  • Year and Date: 2009-06-29
• [Presentation] Geometric Optimization in Grid Topology and Related Combinatorics (2009)
  • Author(s): Takeshi Tokuyama
  • Organizer: 20th Conference on Algorithmic and Combinatorial Geometry
  • Place of Presentation: Budapest
  • Year and Date: 2009-06-18
• [Presentation] An Improved Algorithm for Inserting a Highway in a City Metric Based on Qua-siconvex Optimization (2009)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 京都
  • Year and Date: 2009-04-17
• [Presentation] An Improved Algorithm for Inserting a Highway in a City Metric Based on Quasiconvex Optimization Techniques (2009)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: Proc, of the 2nd Asian Association for Algorithms and Computation (AAAC'09)
  • Place of Presentation: Hangzhou, China
  • Year and Date: 2009-04-11
• [Presentation] An Improved Algorithm for Inserting a Highway in a City Metric Based on Quasiconvex Optimization Techniques (2009)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: Proc, of the 25th European Workshop on Computational Geometry
  • Place of Presentation: Brussels, Belgium
  • Year and Date: 2009-03-16
• [Presentation] Geometric Problems on Ad-Hoc Network Design (2008)
  • Author(s): Takeshi Tokuyama
  • Organizer: RIMS Workshop on Discrete Mathematics and Computational Geometry
  • Place of Presentation: 京都
  • Year and Date: 2008-10-18
• [Presentation] アドホックネットワーク上でのランダム局所近傍を利用した幾何ルーティングアルゴリズムの設計と解析 (2008)
  • Author(s): 佐藤和茂, 徳山豪
  • Organizer: FIT2008報科学技術フォーラム
  • Place of Presentation: 藤原
  • Year and Date: 2008-09-03
• [Presentation] リストページ自動分割問題の最適グラフ分割を用いた解法の提案と評価 (2008)
  • Author(s): 志賀琴枝, 徳山豪
  • Organizer: FIT2008報科学技術フォーラム
  • Place of Presentation: 藤原
  • Year and Date: 2008-09-03
• [Presentation] 動画に対するコメントを利用した自動 Web 検索システム (2008)
  • Author(s): 成田龍太, 全眞嬉, 徳山豪
  • Organizer: FIT2008報科学技術フォーラム
  • Place of Presentation: 藤原
  • Year and Date: 2008-09-03
• [Presentation] Subquadratic Segment Insertion (2008)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: LAシンポジウム2008
  • Place of Presentation: 和歌山
  • Year and Date: 2008-07-23
• [Presentation] Consistent Digital Rays (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Noellenburg, Takeshi Tokuyama
  • Organizer: The 2nd International Symposium on Information Electronics Systems (CERIES-GCOE08)
  • Place of Presentation: Sendai
  • Year and Date: 2008-07-14
• [Presentation] アドホックネットワーク上でのランダム局所近傍を利用した幾何ルーティングアルゴリズムの設計と解析 (2008)
  • Author(s): 佐藤和茂, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 石川
  • Year and Date: 2008-06-16
• [Presentation] Optimal insertion of a segment highway in a city metric (2008)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: Proc, of the 1st Asian Association for Algorithms and Computation (AAAC' 08)
  • Place of Presentation: Hong Kong
  • Year and Date: 2008-04-26
• [Presentation] Digital Star Shapes and Their Applications (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Noellenburg, Takeshi Tokuyama
  • Organizer: Asian Association for Algorithms and Computation 2008 (AAAC' 08)
  • Place of Presentation: Hong Kong
  • Year and Date: 2008-04-26
• [Presentation] Optimal Insertion of a Segment Highway in a City Metric (2008)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: Proc, of the 24th European Workshop on Computational Geometry
  • Place of Presentation: Nancy France
  • Year and Date: 2008-03-19
• [Presentation] Consistent Digital Rays (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Noellenburg, Takeshi Tokuyama
  • Organizer: Proc, of the 24th European Workshop on Computational Geometry
  • Place of Presentation: Nancy France
  • Year and Date: 2008-03-19
• [Presentation] Consistent Digital Rays (2008)
  • Author(s): Jinhee Chun, Matias Korman, Martin Noellenburg, Takeshi Tokuyama
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 神奈川
  • Year and Date: 2008-03-10
• [Presentation] メッシュネットワークにおけるジオメトリックルーティングに関する研究 (2008)
  • Author(s): 小沼寛明, 佐藤和茂, 徳山豪
  • Organizer: 第117アルゴリズム研究会
  • Place of Presentation: 広島
  • Year and Date: 2008-03-07
• [Presentation] Digital Star Shapes and Their Applications (2007)
  • Author(s): Jinhee Chun, Matias Korman, Martin Noellenburg, Takeshi Tokuyama
  • Organizer: 情報処理学会114回アルゴリズム研究会
  • Place of Presentation: 豊橋
  • Year and Date: 2007-09-21
• [Presentation] Optimal Highway Location Problem (2007)
  • Author(s): Matias Korman, Takeshi Tokuyama
  • Organizer: Proc, of the International Conference on Computational Geometry and Graph Theory (CGGT' 07)
  • Place of Presentation: Kyoto
  • Year and Date: 2007-06-12
• [Presentation] Fixed-Parameter Tractability for Non-Crossing Spanning Trees (2007)
  • Author(s): Magnus Halldorsson, Christian Knauer, Andreas Spillner, Takeshi Tokuyama
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 福岡
  • Year and Date: 2007-05-25
• [Presentation] 最適ハイウェイ配置問題 (2007)
  • Author(s): コルマンマティアス, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 福岡
  • Year and Date: 2007-05-25
• [Presentation] 計算理論の現実の場での応用例 (2007)
  • Author(s): 徳山豪
  • Organizer: 情報処理学会春季大会 特別セッション「情報爆発時代における理論と応用」
  • Place of Presentation: 早稲田大学, 東京
  • Year and Date: 2007-03-07
• [Presentation] マグナス ハルドーソン, "Wireless Ad-Hoc ネットワークにおける干渉の軽減法に関する研究" (2007)
  • Author(s): 田代太一, 徳山豪
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 東京
  • Year and Date: 2007-03-05
• [Book] Proceedings of RIMS Workshop on Discrete Mathematics and Computational Geometry (2008)
  • Author(s): Takeshi Tokuyama
• [Book] オンラインアルゴリズムとストリームアルゴリズム (2007)
  • Author(s): 徳山豪
  • Total Pages: 224
  • Publisher: 共立出版
• [Book] Algorithms and Computation, Proc, 18^<th> ISAAC (2007)
  • Author(s): Takeshi Tokuyama, ed
  • Total Pages: 929
  • Publisher: Springer LNCS
• [Remarks] ホームページ等, 東北放送、東北大学の新世紀, 2009年2月16日放映, 「答えより解き方」, 徳山豪
  • URL: http://www.tohoku100-tv.jp/thisweek/090216/index.html
• [Remarks] 東北大学WEBマガジンコラム記事, 「アルゴリズムが世界を動かす」, 2007年10月10日, 徳山豪
  • URL: http://www.tohoku.ac.jp/japanese/webmagazine/column/col-24-tokuyama.html