Algorithms for Geometric Computational Problems Considering Constraints from Practice and Their Applications

2010 Fiscal Year Final Research 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: 計算幾何学 / アルゴリズム / 三角形分割 / 三等分曲線

Research Abstract

In this research we have dealt with the following three problems on computational geometry from a unified point of view. For the first problem we have developed a memory-efficient algorithm for mapping objects in a low-dimensional space so that their dissimilarity is reflected as their distance. For the second problem on triangular mesh we have developed an algorithm based on practical criteria. The third problem is on trisector curves for two points in the plane. We have proved many mathematical properties on the curve together with efficient algorithms for drawing.

Research Products

• [Journal Article] In-place Linear-time Algorithms for Euclidean Distance Transform (2010)
  • Author(s): T.Asano, H.Tanaka
  • Journal Title: LNCS Transactions on Computational Science 8 Pages: 103-113
  • Peer Reviewed
• [Journal Article] Optimal Triangulations of points and segments with steiner points (2010)
  • Author(s): B.Aronov, T.Asano, S.Funke
  • Journal Title: International Journal of Computational Geometry and Applications 20,1 Pages: 89-104
  • Peer Reviewed
• [Journal Article] Disc Covering Problem with Application to Digital Halftoning (2010)
  • Author(s): T.Asano, P.Brass, S.Sasahara
  • Journal Title: Theory of Computing System vol.46,No.2 Pages: 157-173
  • Peer Reviewed
• [Journal Article] Some theoretical challenges in digital geometry : A perspective (2009)
  • Author(s): T.Asano, V.E.Brimkov, R.P.Barneva.
  • Journal Title: Discrete Applied Mathematics 157(16) Pages: 3362-3371
  • Peer Reviewed
• [Journal Article] Finding Nearest Larger Neighbors : A Case Stgudy in Algorithm Design and Analysis (2009)
  • Author(s): T.Asano, S.Bereg, D.Kirkpatrick
  • Journal Title: Lecture Notes in Computer Science("Efficient Algorithms,")(editied by S.Albers, H.Alt, and S.Naeher)(Springer) Pages: 249-260
  • Peer Reviewed
• [Journal Article] Constructing Optimal Highways (2009)
  • Author(s): H.-K.Ahn, H.Alt, T.Asano, S.W.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] Some Generalizations of Least-Squares Algorithms (2009)
  • Author(s): T.Asano, N.Katoh, K.Mehlhorn, T.Tokuyama
  • Journal Title: Statistical Science and Interdiciplinary Research ("Algorithms, Architectures and Information Systems Security,")(edited by B.B.Bhattacharya, S.Sur-Kolay, S.C.Nandy, and A.BaguchiI)(World Scientific Publishers) Vol.3 Pages: 55-74
  • Peer Reviewed
• [Journal Article] Constant-Working-Space Algorithms for Image Processing (2009)
  • Author(s): T.Asano
  • Journal Title: Monograph("ETVC08 : Emerging Trends and Challenges in Visual Computing,")(edited by Frank Nielsen) ETVC2008 Pages: 268-283
  • 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] Constructing Optimal Highways (2009)
  • Author(s): H.-K.Ahn, H.Alt, T.Asano, S.W.Bae, P.Brass, O.Cheong, C.Knauer, H.-S.Na, C.-S Shin, A.Wolff.
  • Journal Title: Int.J.Found.Comput.Sci. 20(1) Pages: 3-23
  • Peer Reviewed
• [Journal Article] Online Uniformity of Integer Points on a Line (2008)
  • Author(s): T.Asano
  • Journal Title: Inf.Process.Lett. 109(1) Pages: 57-60
  • Peer Reviewed
• [Journal Article] Space-Efficient Algorithm for Image Rotation (2008)
  • Author(s): T.Asano, S.Bitou, M.Motoki, N.Usui
  • Journal Title: IEICE Transactions 91-A(9) Pages: 2341-2348
  • Peer Reviewed
• [Journal Article] Voronoi Diagrams with Respect to Criteria on Vision Information (2008)
  • Author(s): T.Asano, N.Katoh, H.Tamaki, T.Tokuyama
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Vol.25 Pages: 1-16
  • Peer Reviewed
• [Journal Article] A Generalization of Magic Squares with Applications to Digital Halftoning (2008)
  • Author(s): B.Aronov, T.Asano, Y.Kikuchi, S.C.Nandy, S.Sasahara, T.Uno
  • Journal Title: Theory of Computing System Volume 42, Number 2 Pages: 143-156
  • Peer Reviewed
• [Journal Article] A Robust Fingerprint Indexing Scheme Using Minutia Neighborhood Structure and Low-order Delaunay Triangles (2007)
  • Author(s): X.Liang, A.Bishnu, T.Asano
  • Journal Title: IEEE Transactions on Information Forensics and Security Volume 2, No.4 Pages: 721-733
  • Peer Reviewed
• [Journal Article] Aspect-Ratio Voronoi Diagram and Its Complexity Bounds (2007)
  • Author(s): T.Asano
  • Journal Title: Information Processing Letters volume 105, Issue 1, 31 Pages: 26-31
  • Peer Reviewed
• [Journal Article] Combinatorial Approach to Fingerprint Binarization and Minutiae Extraction Using Euclidean Distance Transform (2007)
  • Author(s): X.Liang, A.Bishnu, T.Asano
  • Journal Title: International Journal of Pattern Recognition and Artificial Intelligence vol.27,no.7 Pages: 1141-1158
  • 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] The distance trisector curve (2007)
  • Author(s): T.Asano, J.Matousek, T.Tokuyama
  • Journal Title: Advances in Mathematics Vol.212, Issue 1 Pages: 338-360
  • Peer Reviewed
• [Journal Article] In-place Algorithm for Connected Components Labeling
  • Author(s): T.Asano, H.Tanaka
  • Journal Title: Journal of Pattern Recognition Research.(accepted for publication in)
  • Peer Reviewed
• [Journal Article] Constant-Work-Space Image Scan with a Given Angle
  • Author(s): T.Asano
  • Journal Title: Interdisciplinary Information Sciences.(accepted for publication in)
  • Peer Reviewed
• [Presentation] Faster Computation of the Robinson-Foulds Distance between Phylogenetic Networks (2010)
  • Author(s): T.Asano, J.Jansson, K.Sadakane, R.Uehara, G.Valiente
  • Organizer: Proc.21st Combinatorial Pattern Matching(to appear in)
  • Place of Presentation: New york, USA
  • Year and Date: 2010-08-05
• [Presentation] Resource-Constrained Algorithms : Space-Time Tradeoffs (2010)
  • Author(s): T.Asano
  • Organizer: Proc.WAAC 2010, Korea-Japan Workshop on Algorithms and Computation, pp.190-201
  • Place of Presentation: Kanazawa, Japan
  • Year and Date: 2010-07-05
• [Presentation] Do We Need a Stack to Erase a Component in a Binary Image? (2010)
  • Author(s): T.Asano
  • Organizer: Fifth International Conference on FUN WITH ALGORITHMS, pp.16-27
  • Place of Presentation: Ischia, Italy
  • Year and Date: 2010-06-02
• [Presentation] Kaboozle is NP-complete, even in a Strip Form (2010)
  • Author(s): T.Asano, E.D.Demaine, M.L.Demaine, R.Uehara
  • Organizer: Fifth International Conference on FUN WITH ALGORITHMS, pp.28-36
  • Place of Presentation: Ischia, Italy
  • Year and Date: 2010-06-02
• [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, WALCOM, Dhaka, Bangladesh, pp.9-20, February 2010 (Lecture Notes of Computer Science, LNCS 5942, Springer)
  • Place of Presentation: Dhakka, Pakistan(Invited talk)
  • Year and Date: 2010-02-08
• [Presentation] Constant Working-Space Algorithms for Geometric Problems (2009)
  • Author(s): T.Asano, G.Rote.
  • Organizer: Proc.Canadian Conference on Computational Geometry, pp.87-90
  • Place of Presentation: Vancouver, Canada
  • Year and Date: 2009-08-13
• [Presentation] Constant-Working-Space Algorithms for Image Processing (2008)
  • Author(s): T.Asano
  • Organizer: ETVC08 : Emerging Trends and Challenges in Visual Computing, Ecole Polytechnique
  • Place of Presentation: Paris, France
  • Year and Date: 20081118-20081120
• [Presentation] Constant Working Space Algorithms with Applications (2008)
  • Author(s): T.Asano
  • Organizer: Abstracts of 5th International Conference of Applied Mathematics and Computing, p.1-47
  • Place of Presentation: Plvdiv, Bulgaria
  • Year and Date: 20080812-20080818
• [Presentation] Constant-Working Space Algorithm for Image Processing (2008)
  • Author(s): T.Asano
  • Organizer: Proc.of the First AAAC Annual meeting, p.3
  • Place of Presentation: Hong Kong
  • Year and Date: 20080426-20080427
• [Presentation] Linear Boundary and Corner detection using limited number of sensor rows (2008)
  • Author(s): B.Prasad, A.Bishnu, T.Asano
  • Organizer: Proc.IWCIA (Int.Workshop on Combinatorial Image Analysis) 2008, pp.250-261
  • Place of Presentation: Buffalo, USA
  • Year and Date: 20080407-20080409
• [Presentation] Constant-Working-Space Image Scan with a Given Angle (2008)
  • Author(s): T.Asano
  • Organizer: Proc.24th European Workshop on Computational Geometry, pp.165-168
  • Place of Presentation: Nancy, France.
  • Year and Date: 20080318-20080320
• [Presentation] Online Uniformity of Integer Points on a Line (2008)
  • Author(s): T.Asano
  • Organizer: Proc.24th European Workshop on Computational Geometry, pp.99-102
  • Place of Presentation: Nancy, France.
  • Year and Date: 20080318-20080320
• [Presentation] Constant-Working-Space Algorithms : How Fast Can We Solve Problems without Using Any Extra Array? (2008)
  • Author(s): T.Asano
  • Organizer: ISAAC 2008,p.1
  • Place of Presentation: Goldcoast, Australia(招待講演)
  • Year and Date: 2008-12-20
• [Presentation] Constant-Working-Space Algorithms (2008)
  • Author(s): T.Asano
  • Organizer: Proc.Kyoto RIMS International Workshop on Computational Geometry and Discrete Mathematics
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2008-10-15
• [Presentation] Dissimilarity Preserving Embedding of Objects on the Plane (2007)
  • Author(s): T.Asano
  • Organizer: Invited Talk at International Xu Guangqi Conference
  • Place of Presentation: Shanghai, China
  • Year and Date: 20071014-20071019
• [Presentation] Optimal Triangulation with Steiner Points (2007)
  • Author(s): B.Aronov, T.Asano, S.Funke
  • Organizer: Proc.ISAAC 2007, pp.681-691
  • Place of Presentation: Sendai, Japan
  • Year and Date: 2007-12-19
• [Presentation] In-Place Algorithm for Image Rotation (2007)
  • Author(s): T.Asano, S.Bitou, M.Motoki, N.Usui
  • Organizer: Proc.ISAAC 2007, pp.704-715
  • Place of Presentation: Sendai, Japan
  • Year and Date: 2007-12-19
• [Presentation] On-line uniformity of points (2007)
  • Author(s): T.Asano, S.Teramoto
  • Organizer: Book of Abstracts for 8th Hellenic-European Conference on Computer Mathematics and its Applications, pp.21-22
  • Place of Presentation: Athens, Greece
  • Year and Date: 2007-09-05
• [Presentation] Linear-Space Algorithms for Distance Preserving Embedding (2007)
  • Author(s): T.Asano, P.Bose, P.Carmi, A.Maheshwari, C.Shu, M.Smid, S.Wuhrer
  • Organizer: Canadian Conference on Computational Geometry, pp.185-188
  • Place of Presentation: Ottawa, Canada
  • Year and Date: 2007-08-22
• [Presentation] Voronoi Diagram with Respect to Criteria on Vision Information (2007)
  • Author(s): T.Asano, N.Katoh, H.Tamaki, T.Tokuyama
  • Organizer: Proc.the 4th International Symposium on Voronoi Diagrams in Science and Engineering, pp.25-32
  • Place of Presentation: Pontypridd, Wales, UK
  • Year and Date: 2007-07-09
• [Remarks] ホームページ等