Continuous Optimization Approach to Discrete Decision Problems

• Project/Area Number: 15H06286
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Toyohashi University of Technology
• Principal Investigator: Kimura Kei 豊橋技術科学大学, 工学(系)研究科(研究院), 助教 (00758716)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 制約充足問題 / アルゴリズム / 数理計画法

Outline of Final Research Achievements

In this research project, we obtained the following results.
(1) We analyzed the applicability of linear program to the constraint satisfaction problem and proposed an algorithm to find a satisfiability preserving assignment. (2) We applied the result (1) to Horn CNFs and obtained a linear time algorithm to find a linear autark assignment. (3) We revealed the computational complexity of optimal matroid partitioning problems under various objective functions. (4) We revealed the computational complexity of three discrete puzzles.

Research Products

• [Journal Article] Autark assignments of Horn CNFs (2018)
  • Author(s): Kei Kimura and Kazuhisa Makino
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 35 Issue: 1 Pages: 297-309
  • DOI: 10.1007/s13160-017-0284-6
  • NAID: 210000163987
  • Peer Reviewed
• [Journal Article] Linear Satisfiability Preserving Assignments (2018)
  • Author(s): Kei Kimura and Kazuhisa Makino
  • Journal Title: Journal of Artificial Intelligence Research Volume: 61 Pages: 291-321
  • Peer Reviewed / Open Access
• [Journal Article] Trichotomy for Integer Linear Systems Based on Their Sign Patterns (2016)
  • Author(s): Kei Kimura and Kazuhisa Makino
  • Journal Title: Discrete Applied Mathematics Volume: VOL.200 Pages: 67-78
  • DOI: 10.1016/j.dam.2015.07.004
  • Peer Reviewed
• [Presentation] The Fewest Clues Problem of Picross 3D (2018)
  • Author(s): Kei Kimura, Takuya Kamehashi, and Toshihiro Fujito
  • Organizer: The 9th International Conference on Fun with Algorithms
  • Int'l Joint Research
• [Presentation] Optimal Matroid Partitioning Problems (2017)
  • Author(s): Yasushi Kawase, Kei Kimura, Kazuhisa Makino, and Hanna Sumita
  • Organizer: The 28th International Symposium on Algorithms and Computation
  • Int'l Joint Research
• [Presentation] Min-sum-max matroid partitioning problem (2017)
  • Author(s): Yasushi Kawase, Kei Kimura, Kazuhisa Makino, and Hanna Sumita
  • Organizer: The 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Int'l Joint Research