Algorithms for Solving Geometric Problems Considering Constraints from Practice and Their Application

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19300002
• 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: Japan Advanced Institute of Science and Technology
• Principal Investigator: ASANO Tetsuo Japan Advanced Institute of Science and Technology, 情報科学研究科, 教授 (90113133)
• Project Period (FY): 2007 – 2010
• Keywords: アルゴリズム / 計算幾何学 / 三角形メッシュ / 距離情報

Research Abstract

本研究は,現実的な制約を考慮に入れつつも,計算幾何の諸問題を効率よく解く解法を開発しようとするものである.具体的には計算幾何学における下記の3問題について統一的な視点から研究を進める.
A.距離情報から点の座標を求める問題とその応用
対象物間の非類似度を距離行列の形で入力して,距離を最大限保存する形で対象物を低次元空間の点に埋め込むためのアルゴリズムを提案し,実装まで行って計算機実験を行い,その効果を検証する.
B.三角形メッシュ改善問題とその応用
本研究では有限要素法などで重要な三角形のアスペクト比(最長辺と最小の高さの比)に基づいたメッシュ改善法を提案する.一般の多角形に対しては問題が困難であるので,対象となる多角形を限定して研究を進める.
C.三等分曲線の計算問題とその応用
与えられた2点の間を三等分する曲線を厳密な意味で求めることが非常に困難であることは申請者らの以前の研究成果で明らかであるが,本研究では更に判定不能問題とも絡めて議論する.

Research Products

• [Journal Article] Disc Covering Problem with Application to Digital Halftoning (2010)
  • Author(s): T. Asano, Peter Brass, Shinji Sasahara
  • Journal Title: Theory of Computing System vol.46,No.2 Pages: 157-173
  • Peer Reviewed
• [Journal Article] Finding Nearest Larger Neighbors : A Case Stgudy in Algorithm Design and Analysis (2009)
  • Author(s): Tetsuo Asano, Sergey Bereg, David Kirkpatrick
  • Journal Title: Lecture Notes in Computer Science, "Efficient Algorithms," Pages: 249-260
  • Peer Reviewed
• [Journal Article] Constructing Optimal Highways (2009)
  • Author(s): Hee-Kap Ahn, Helmut Alt, Tetsuo Asano, Sang Won Bae, Peter Brass, Otfried Cheong, Christian Knauer, Hyeon-Suk Na, Chan-Su Shin, Alexander Wolff
  • Journal Title: Internat.J.Found.Comput.Sci. 20, 1 Pages: 3-23
  • Peer Reviewed
• [Journal Article] A Linear-Space Algorithm for Distance Preserving Graph Embedding (2009)
  • Author(s): T. Asano, P. Bose, P. Carmi, A. Maheshwari, C. Shu, M. Smid, S. Wuhrer
  • Journal Title: Computational Geometry : Theory and Applications 42(4) Pages: 289-304
  • Peer Reviewed
• [Journal Article] Zone diagrams : Existence, Uniqueness and Algorithmic Challenge (2007)
  • Author(s): T. Asano, J. Matousek, T. Tokuyama
  • Journal Title: SIAM J.on Computing Vol.37, Issue 4 Pages: 1182-1198
  • Peer Reviewed
• [Journal Article] Optimal Triangulations of points and segments with steiner points
  • Author(s): B. Aronov, T. Asano, S. Funke
  • Journal Title: International Journal of Computational Geometry and Applications
  • Peer Reviewed
• [Presentation] Faster Computation of the Robinson-Foulds Distance between Phylogenetic Networks (2010)
  • Author(s): Tetsuo Asano, Jesper Jansson, Kunihiko Sadakane, Ryuhei Uehara, Gabriel Valiente
  • Organizer: Proc.21st Combinatorial Pattern Matching, 2010
  • Place of Presentation: New York(発表決定)
  • Year and Date: 2010-06-24
• [Presentation] Constant-Work-Space Algorithm for a Shortest Path in a Simple Polygon (2010)
  • Author(s): T. Asano, W. Mulzer, Y. Wang
  • Organizer: Proc.4th International Workshop on Algorithms and Computation
  • Place of Presentation: WALCOM, Dhaka, Bangladesh(Invited talk)
  • Year and Date: 2010-02-10
• [Presentation] Constant Working-Space Algorithms for Geometric Problems (2009)
  • Author(s): Tetsuo Asano, Guenter Rote
  • Organizer: Proc.Canadian Conference on Computational Geometry
  • Place of Presentation: Vancouver
  • Year and Date: 2009-08-15
• [Presentation] Online Uniformity of Integer Points on a Line (2008)
  • Author(s): T. Asano
  • Organizer: Proc.24th European Workshop on Computational Geometry
  • Place of Presentation: Nancy, France
  • Year and Date: 20080318-20080320
• [Presentation] Optimal Triangulation with Steiner Points (2007)
  • Author(s): Boris Aronov, Tetsuo Asano, Stefan Funke
  • Organizer: Proc.ISAAC 2007
  • Place of Presentation: Sendai
  • Year and Date: 20071217-20071219