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Research on Geometric Data Processing via Parametric Optimization

Research Project

Project/Area Number 13680387
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionTohoku University

Principal Investigator

TOKUYAMA Takeshi  Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (40312631)

Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsParametric Optimization / Computational Geometry / Theoretical Computer Science / Data Mining / Algorithms / Discrete Mathematics / Halftoning / 多次元パラメトリック探索 / データ分割 / アレンジメント
Research Abstract

We have published seventeen refereed papers during the term. We established the framework of parametric optimization, and give a new paradigm for the multi-dimensional parametric searching. We also work on the combinatorics of hyperplane arrangement, which is foundation of the theory : As new results, we give complexity analysis of levels of three dimensional arrangements, and also give new efficient algorithms for searching peaks of k-level of an arrangement. Moreover, we have investigated use of parametric optimization in quantum computation. As applications of parametric optimization, we have investigated data mining, digital halftoning, and image segmentation. Besides theoretical results, we have done system construction in data mining application. These research results were published in authorized journals and conferences such as ACM STOC,ACM SCG,ACM-SIAM SODA,ISAAC,SIAM Journal on Computing, ACM Transaction, and Discrete & Computational Geometry.
We have also given several talks in International/National conferences and workshops on the topics related to this project.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (56 results)

All Other

All Publications (56 results)

  • [Publications] Takeshi Fukuda, Yasuhiko Morimoto, Shin-ich Morishita, Takeshi Tokuyama: "Data Mining with Optimized Two-Dimensional Association Rules"ACM Transaction on Database Systems. 26. 179-213 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Asano, Naoki Katoh, Takeshi Tokuyama: "A Unified Scheme for Detecting Fundamental Curves in Binary Edge Image"Computational Geometry, Theory and Applications. 11-2. 73-93 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuo Asano, Danny Chen, Naoki Katoh, Takeshi Tokuyama: "Efficient Algorithms for Optimization-Based Image Segmentation"Computational Geometry, Theory and Applications. 11-2. 145-166 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuo Asano, Takeshi Tokuyama: "On Detecting Digital Line Images in a Binary Image"IEICE Transaction, Fundamental. 84-A. 1120-1129 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Tokuyama: "Minimax Parametric Optimization Problems and Multi-Dimensional Parametric Searching"Proceedings of 33rd ACM Symposium on Theory of Computing. 33. 75-83 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Naoki Katoh, Takeshi Tokuyama: "Notes on Computing Peaks in K-Levels and Parametric Spanning Trees"Proceedings of 17^<th> ACM Symposium on Computational Geometry. 17. 241-248 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Naoki Katoh, Takeshi Tokuyama: "K-Levels of Concave Surfaces"Discrete and Computational Geometry. 27-4. 567-584 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yasuhiko Morimoto, Takeshi Fukuda, Takeshi Tokuyama: "Algorithms for Finding Attribute Value Group for Binary Segmentation of Categorical Databases"IEEE Transaction on Knowledge and Data Engineering. 14-6. 1269-1279 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kunihiko Sadakane, Nadia Takki-Chebihi, Takeshi Tokuyama: "Discrepancy-Based Digital Halftoning : Automatic Evaluation and Optimization"Interdisciplinary Information Sciences. 8-2. 219-234 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kunihiko Sadakane, Norito Sugawara, Takeshi Tokuyama: "Quantum Computation in Computational Geometry"Interdisciplinary Information Sciences. 8-2. 129-136 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama: "Parametric Polymatroid Optimization and Its Geometric Applications"International Journals of Computational Geometry and Applications. 12-5. 429-443 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Tokuyama: "Efficient Algorithms for the Minimum Diameter Bridge Problem"Computational Geometry Theory and Applications. 24-1. 11-18 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuo Asano, Naoki Katoh, Koji Obokata, Takeshi Tokuyama: "Matrix Rounding under the Lp Discrepancy Measure and Its Application to Digital Halftoning"SIAM Journal on Computing. 32-6. 1423-1435 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hisao Tamaki, Takeshi Tokuyama: "A Characterization of Planar Graphs by Pseudo-Line Arrangement"Algorithmica. 35. 269-286 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama: "The Structure and Number of Global Roundings of a Graph"Proceedings of 9^<th> International Conference on Computing and Combinatorics. LNCS2697. 130-138 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Jinhee Chun, Kunihiko Sadakane, Takeshi Tokuyama: "Linear Time Algorithm for Approximating a Curve by a Single-Peaked Curve"Proceedings of 14th International Symposium on Algorithms and Computation. LNCS2906. 6-15 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nadia Takki-Chebihi, Takeshi Tokuyama: "Enumerating Global Roundings of an Outerplanar Graph"Proceedings of 14th International Symposium on Algorithms and Computation. LNCS2906. 425-433 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 徳山 豪: "離散数学とその応用"数理工学社. 213 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Fukuda, Y.Morimoto, S.Morishita, T.Tokuyama: "Data mining using twodimensional optimized association rules"ACM Trans.on Database Systems. 26. 179-213 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Asano, N.Katoh, T.Tokuyama: "Unified Scheme for Detecting Fundamental Curves in Binary Edgel Image"Comput.Geom.Theory and Appl.. 11-2. 73-93 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Asano, D.Z.Chen, N.Katoh, T.Tokuyama: "Efficient Algorithms for Optimization-Based Image Segmentation"Comput.Geom.Theory and Appl.. 11-2. 145-166 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Asano, T.Tokuyama: "On Detecting digital Line Images in a Binary Image"IEICE Transaction Fundamental. 84-A. 1120-1129 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Tokuyama: "Minimax Parametric Optimization Problems and Multi-Dimensional Parametric Searching"Proc.33^<rd> ACM Symp.on Theory of Computation. 33. 75-83 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Katoh, T.Tokuyama: "Notes on Computing Peaks in K-Levels and Parametric Spanning Trees"Proc.17^<rd> ACM Symp.on Comput.Geom.. 17. 241-248 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Katoh, T.Tokuyama: "K-Levels of Concave Surfaces"Discrete & Comput.Geom.. 27-4. 567-584 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morimoto, T.Fukuda, T.Tokuyama: "Algorithms for Finding Attribute Value Group for Binary Segmentation of Categorical Databases"IEEE Trans.on Knowledge and Data Engineering. 14-6. 1269-1279 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Sadakane, N.Takki-Chebihi, T.Tokuyama: "Discrepancy based digital halftoning: automatic evaluation and optimization"Interdis.Inform.Sciences. 8-2. 219-234 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Sadakane, N.Sugawara, T.Tokuyama: "Quantum Computation in computational Geometry"Interdis.Inform.Sciences. 8-2. 219-234 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Katoh, H.Tamaki, T.Tokuyama: "Parametric Polymatroid Optimization and Its Geometric Applications"Int.J.Comput.Geom.and Appl.. 12-5. 429-443 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Tokuyama: "Efficient Algorithms for the Minimum Diameter Bridge Problems"Comput.Geom.,Theory and Appl.. 24-1. 11-18 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Asano, N.Katoh, K.Obokata, T.Tokuyama: "Matrix Rounding under the Lp-Discrepancy Measure and Its Application to Digital Halftoning"SIAM Journal on Computing. 32-6. 1423-1435 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Tamaki, T.Tokuyama: "A Characterization of Planar Graphs by Pseudoline Arrangement"Algorithmica. 35. 269-286 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Asano, N.Katoh, H.Tamaki, T.Tokuyama: "The Structure and Number of Global Roundings of A Graph"Proc.9^<th> Int.Conf.COCOON'03, LNCS. 2697. 130-138 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.Chun, K.Sedakane, T.Tokuyama: "Linear Time Algorithms for Approximating a Curve by a Single-Peaked Curve"Proc.14^<th> Int.Symp ISAAC'03, LNCS. 2906. 6-15 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Takki-chebihi, T.Tokuyama: "Enumerating Global Roundings of an Outerplanar Graph"Proc.14^<th> Int.Symp ISAAC'03, LNCS. 2906. 425-433 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Tokuyama: "Discrete Mathematics and Its Applications (Book, In Japanese)"Suri-Kogaku sha publishing. 213 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Tokuyama: "Efficient Algorithms for the Minimum Diameter Bridge Problem"Computational Geometry. 24-1. 11-18 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsuo Asano, Naoki Katoh, Koji Obokata, Takeshi Tokuyama: "Matrix Rounding under the Lp Discrepancy Measure and Its Application to Digital Halftoning"SIAM Journal on Computing. 32-6. 1423-1435 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hisao Tamaki, Takeshi Tokuyama: "A Characterization of Planar Graphs by Pseudo-Line Arrangements"Algorithmica. 35. 269-286 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Nadia Takki-Chebihi, Takeshi Tokuyama: "Enumerating Global Roundgs of an Outerplanar Graph"Proceedings of 14th International Symposium on Algorithms and Computation. LNCS2906. 425-433 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Jinhee Chun, Kunihiko Sadakane, Takeshi Tokuyama: "Linear Time Algorithm for Approximating a Curve by a Single-Peaked Curve"Proceedings of 14th International Symposium on Algorithms and Computation. LNCS2906. 6-15 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama: "The Structure and Number of Global Roundings of a Graph"Computing and Combinatorics, 9th Annual International Conference. LNCS2697. 130-138 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 徳山 豪: "離散数学とその応用"数理工学社. 213 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Naoki Katoh, Takeshi Tokuyama: "K-Levels of Concave Surfaces"Discrete and Computational Geometry. 27-4. 567-584 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama: "Parametric Polymatroid Optimization and Its Geometric Applications"International Journal of Compjutational Geometry and Applications. 12-5. 429-443 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Yasuhiko Morimoto, Takeshi Fukuda, Takeshi Tokuyama: "Algorithms for Finding Attribute Value Group for Binary Segmentation of Categorical Databases"IEEE Transaction on Knowledge and Data Engineering. 14-6. 1269-1279 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tetsuo Asano, Naoki Katoh, Koji Obokata, Takeshi Tokuyama: "Matrix Rounding under the Lp-Discrepancy Measure and Its Application to Digital Halftoning"ACM-SIAM Symposium on Discrete Algorithms. 13. 894-904 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kunihiko Sadakane, Nadia Takki Chebihi, Takeshi Tokuyama: "Discrepancy-Based Digital Halftoning : Automatic Evaluation and Optimization"Interdisciplinary Information Sciences. 8-2. 219-234 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kunihiko Sadakane, Norito Sugawara, Takeshi Tokuyama: "Quantum Computation in Computational Geometry"Interdisciplinary Information Sciences. 8-2. 129-136 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tetsuo Asano, Naoki Katoh, Takeshi Tokuyama: "A unified scheme for detecting fundamental curves in binary edge images"Computational Geometry Theory and Applications. 18. 73-93 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Tetsuo Asano, Danny Chen, Naoki Katoh, Takeshi Tokuyama: "Efficient algorithms for optimization-based image segmentation"International Journal of Compjutational Geometry and Applications. 11-2. 145-166 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Tetsuo Asano, Takeshi Tokuyama: "On detecting digital line component in a binary image"IEICE Transaction,Fundamental. 84-A. 1120-1129 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Fukuda, Y.Morimoto, S.Morishita, Takeshi Tokuyama: "Data Mining with optimized two-dimensional association rules"ACM Transaction of Database Systems. 26. 179-213 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takeshi Tokuyama: "Minimax parametric optimization problems and multi-dimensional parametric searching"Proceedings of 33rd ACM Symposium on Theory of Computing. 33. 75-83 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Naoki Katoh, Takeshi Tokuyama: "Notes on computing peaks in k-levels and parametric spanning trees""Proceedings of 17th ACM Symposium on Computational Geometry. 17. 241-248 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 福田 剛志, 森本 康彦, 徳山 豪: "データマイニング"共立出版. 169 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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