Hierarchical results on complexity classes and methods for evaluating logic synthesis systems

• Project/Area Number: 16K00020
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Hiroshima University
• Principal Investigator: Iwamoto Chuzo 広島大学, 先進理工系科学研究科(工), 教授 (60274495)
• Project Period (FY): 2016-04-01 – 2022-03-31
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 計算複雑性 / 計算複雑さ / 計算の複雑さ / 計算量理論

Outline of Final Research Achievements

It is strongly believed that in order to solve more difficult problems, we need more computational resources, such as space and time. Studies on hierarchies of complexity classes provide a theoretical evidence for such properties. In this research, we studied the computational complexity of several combinatorial problems, and proved that some of those problems are NP-hard. We also proposed placement algorithms which assign a set of minimum guards on a given polygon, and discussed the complexity of the placement problem.

Academic Significance and Societal Importance of the Research Achievements

理論計算機科学の分野で最も重要かつ有名な未解決問題はＰ≠ＮＰ予想の証明である．本予想は，ミレニアム懸賞問題としてアメリカのクレイ数学研究所によって100万ドルの懸賞金がかけられている７問題の一つである．本研究では，どのような問題がＮＰ完全になるのか，または多項式時間で解ける問題のクラスＰに属するのかを探究することで，予想の証明の手がかりを探った．その結果，十数個の組合せ問題がＮＰ完全になることを解明できた．

Research Products

• [Journal Article] Five Cells and Tilepaint are NP-Complete (2022)
  • Author(s): IWAMOTO Chuzo、IDE Tatsuya
  • Journal Title: IEICE Transactions on Information and Systems Volume: E105.D Issue: 3 Pages: 508-516
  • DOI: 10.1587/transinf.2021FCP0001
  • NAID: 130008165595
  • ISSN: 0916-8532, 1745-1361
  • Year and Date: 2022-03-01
  • Peer Reviewed
• [Journal Article] Moon-or-Sun, Nagareru, and Nurimeizu are NP-complete (2022)
  • Author(s): Chuzo Iwamoto、Tatsuya Ide
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E105.A Pages: 1-8
  • Peer Reviewed
• [Journal Article] Vertex-to-Point Conflict-Free Chromatic Guarding is NP-Hard (2022)
  • Author(s): Iwamoto Chuzo、Ibusuki Tatsuaki
  • Journal Title: Lecture Notes in Computer Science, Springer-Verlag Volume: 13174 Pages: 111-122
  • DOI: 10.1007/978-3-030-96731-4_10
  • ISBN: 9783030967307, 9783030967314
  • Peer Reviewed
• [Journal Article] Computational Complexity of Two Pencil Puzzles: Kurotto and Juosan (2021)
  • Author(s): Iwamoto Chuzo、Ibusuki Tatsuaki
  • Journal Title: Lecture Notes in Computer Science, Springer-Verlag Volume: 13034 Pages: 175-185
  • DOI: 10.1007/978-3-030-90048-9_14
  • ISBN: 9783030900472, 9783030900489
  • Peer Reviewed
• [Journal Article] Chromatic Art Gallery Problem with r-visibility is NP-complete (2021)
  • Author(s): Chuzo Iwamoto, Tatsuaki Ibusuki
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E104-A Pages: 1-8
  • Peer Reviewed
• [Journal Article] Computational Complexity of Nurimisaki and Sashigane (2020)
  • Author(s): IWAMOTO Chuzo、IDE Tatsuya
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E103.A Issue: 10 Pages: 1183-1192
  • DOI: 10.1587/transfun.2019DMP0002
  • NAID: 130007920259
  • ISSN: 0916-8508, 1745-1337
  • Year and Date: 2020-10-01
  • Peer Reviewed
• [Journal Article] Polynomial-Time Reductions from 3SAT to Kurotto and Juosan Puzzles (2020)
  • Author(s): Chuzo Iwamoto and Tatsuya Ibusuki
  • Journal Title: IEICE Transactions on Information and Systems Volume: E103.D Issue: 3 Pages: 500-505
  • DOI: 10.1587/transinf.2019FCP0004
  • NAID: 130007804165
  • ISSN: 0916-8532, 1745-1361
  • Year and Date: 2020-03-01
  • Peer Reviewed
• [Journal Article] Computational Complexity of the Chromatic Art Gallery Problem for Orthogonal Polygons (2020)
  • Author(s): Iwamoto Chuzo、Ibusuki Tatsuaki
  • Journal Title: Lecture Notes in Computer Science Volume: 12049 Pages: 146-157
  • DOI: 10.1007/978-3-030-39881-1_13
  • ISBN: 9783030398804, 9783030398811
  • Peer Reviewed
• [Journal Article] Computational Complexity of Herugolf and Makaro (2019)
  • Author(s): Chuzo Iwamoto, Masato Haruishi, and Tatsuya Ibusuki
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E102.A Issue: 9 Pages: 1118-1125
  • DOI: 10.1587/transfun.E102.A.1118
  • NAID: 130007699568
  • ISSN: 0916-8508, 1745-1337
  • Year and Date: 2019-09-01
  • Peer Reviewed
• [Journal Article] Computational Complexity of Usowan Puzzles (2018)
  • Author(s): Chuzo Iwamoto and Masato Haruishi
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E101.A Issue: 9 Pages: 1537-1540
  • DOI: 10.1587/transfun.E101.A.1537
  • NAID: 130007479526
  • ISSN: 0916-8508, 1745-1337
  • Year and Date: 2018-09-01
  • Peer Reviewed
• [Journal Article] Dosun-Fuwari is NP-complete (2018)
  • Author(s): Chuzo Iwamoto and Tatsuaki Ibusuki
  • Journal Title: Journal of Information Processing Volume: 26 Issue: 0 Pages: 358-361
  • DOI: 10.2197/ipsjjip.26.358
  • NAID: 130006707935
  • ISSN: 1882-6652
  • Peer Reviewed
• [Journal Article] NP-completeness of Mojipittan (2017)
  • Author(s): 岩本宙造，春石聖人
  • Journal Title: 電子情報通信学会論文誌D 情報・システム Volume: J100-D Issue: 12 Pages: 974-977
  • DOI: 10.14923/transinfj.2017JDL8016
  • ISSN: 1880-4535, 1881-0225
  • Year and Date: 2017-12-01
  • Peer Reviewed
• [Journal Article] Finding the Minimum Number of Open-Edge Guards in an Orthogonal Polygon is NP-Hard (2017)
  • Author(s): Chuzo Iwamoto
  • Journal Title: IEICE Transactions on Information and Systems Volume: E100.D Issue: 7 Pages: 1521-1525
  • DOI: 10.1587/transinf.2016EDL8251
  • NAID: 130006792955
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed
• [Journal Article] Computational Complexity of Building Puzzles (2016)
  • Author(s): Chuzo Iwamoto and Yuta Matsui
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E99.A Issue: 6 Pages: 1145-1148
  • DOI: 10.1587/transfun.E99.A.1145
  • NAID: 130005154236
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Presentation] Vertex-to-Point Conflict-Free Chromatic Guarding is NP-hard (2022)
  • Author(s): Chuzo Iwamoto
  • Organizer: The 16th International Conference and Workshops on Algorithms and Computation
  • Int'l Joint Research
• [Presentation] Moon-or-Sun, Nagareru, and Nurimeizu are NP-complete (2020)
  • Author(s): 井出達也，岩本宙造
  • Organizer: 冬のＬＡシンポジウム
• [Presentation] Computational Complexity of the Chromatic Art Gallery Problem for Orthogonal Polygons (2020)
  • Author(s): 岩本宙造
  • Organizer: 冬のＬＡシンポジウム
• [Presentation] Nurimisaki and Sashigane are NP-complete (2019)
  • Author(s): Chuzo Iwamoto
  • Organizer: The 31st Canadian Conference on Computational Geometry
  • Int'l Joint Research
• [Presentation] Kurotto and Juosan are NP-complete (2018)
  • Author(s): Chuzo Iwamoto
  • Organizer: The 21st Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG^3 2018)
  • Int'l Joint Research
• [Presentation] Herugolf and Makaro are NP-complete (2018)
  • Author(s): Chuzo Iwamoto
  • Organizer: The Ninth International Conference on Fun with Algorithms (FUN 2018)
  • Int'l Joint Research