Studies on Algorithms for Generalized Tree Construction Problems

• Project/Area Number: 23700014
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Fundamental theory of informatics
• Research Institution: Shinshu University (2014-2015); Toyohashi University of Technology (2011-2013)
• Principal Investigator: FUJIWARA Hiroshi 信州大学, 学術研究院工学系, 准教授 (80434893)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: アルゴリズム / 組合せ最適化 / 数理工学 / 情報基礎 / モデル化 / オンライン最適化 / 最適化 / 木

Outline of Final Research Achievements

We consider a problem that generalizes the famous Huffman Tree Problem by associating each leaf with an arbitrary function. If the functions are all linear, then the problem can be solved in polynomial time by Huffman's algorithm. On the other hand, it is known that the problem is NP-hard for general functions. We design a polynomial-time algorithm for the case of unit step functions. Moreover, we show limitations in improvement of algorithms for several related optimization problems.

Research Products

• [Journal Article] Competitive Analysis for the Flat-Rate Problem (2016)
  • Author(s): Hiroshi Fujiwara, Atsushi Matsuda, and Toshihiro Fujito
  • Journal Title: IEICE Transactions on Information and Systems Volume: E99.D Issue: 3 Pages: 559-566
  • DOI: 10.1587/transinf.2015FCP0005
  • NAID: 130005131810
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Online Weight Balancing on the Unit Circle (2016)
  • Author(s): Hiroshi Fujiwara, Takahiro Seki, and Toshihiro Fujito
  • Journal Title: IEICE Transactions on Information and Systems Volume: E99.D Issue: 3 Pages: 567-574
  • DOI: 10.1587/transinf.2015FCP0006
  • NAID: 130005131814
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The Huffman Tree Problem with Unit Step Functions (2015)
  • Author(s): H. Fujiwara, T. Nakamura, T. Fujito
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E98.A Issue: 6 Pages: 1189-1196
  • DOI: 10.1587/transfun.E98.A.1189
  • NAID: 130005071830
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the Best Possible Competitive Ratio for the Multislope Ski-Rental Problem (2014)
  • Author(s): Hiroshi Fujiwara, Takuma Kitano, and Toshihiro Fujito
  • Journal Title: Journal of Combinatorial Optimization (JOCO) Volume: Online ISSN 1573-2886 Issue: 2 Pages: 463-490
  • DOI: 10.1007/s10878-014-9762-9
  • NAID: 120007100502
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Analysis of Lower Bounds for the Multislope Ski-Rental Problem (2014)
  • Author(s): Hiroshi Fujiwara, Yasuhiro Konno, and Toshihiro Fujito
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E97.A Issue: 6 Pages: 1200-1205
  • DOI: 10.1587/transfun.E97.A.1200
  • NAID: 130004770849
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Improved Lower Bounds for the Online Bin Packing Problem with Cardinality Constraints (2013)
  • Author(s): H. Fujiwara, K. Kobayashi
  • Journal Title: Journal of Combinatorial Optimization Volume: Online ISSN 1573-2886 Issue: 1 Pages: 1-21
  • DOI: 10.1007/s10878-013-9679-8
  • NAID: 120007100503
  • Peer Reviewed
• [Journal Article] Collision Probability in an In-Line Equipment Model under Erlang Distribution (2013)
  • Author(s): Eishi Chiba, Hiroshi Fujiwara, Yoshiyuki Sekiguchi, and Toshihide Ibaraki
  • Journal Title: IEICE Transactions on Information and Systems Volume: E96.D Issue: 3 Pages: 400-407
  • DOI: 10.1587/transinf.E96.D.400
  • NAID: 10031167424
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed
• [Journal Article] On the Huffman and Alphabetic Tree Problem with General Cost Functions (2013)
  • Author(s): Hiroshi Fujiwara and Tobias Jacobs
  • Journal Title: Algorithmica Volume: Online ISSN 1432-0541 Issue: 3 Pages: 582-604
  • DOI: 10.1007/s00453-013-9755-6
  • NAID: 120007100504
  • Peer Reviewed
• [Journal Article] An improved analysis of SRPT scheduling algorithm on the basis of functional optimization (2012)
  • Author(s): Hiroshi Fujiwara, Yoshiyuki Sekiguchi
  • Journal Title: Information Processing Letters Volume: 112 Issue: 23 Pages: 911-915
  • DOI: 10.1016/j.ipl.2012.08.009
  • NAID: 120007100507
  • Peer Reviewed
• [Journal Article] Average-Case Competitive Analyses for One-Way Trading (2011)
  • Author(s): Hiroshi Fujiwara, Kazuo Iwama, and Yoshiyuki Sekiguchi
  • Journal Title: Journal of Combinatorial Optimization (JCO) Volume: Vol. 21, No. 1 Issue: 1 Pages: 83-107
  • DOI: 10.1007/s10878-009-9239-4
  • NAID: 120007100508
  • Peer Reviewed
• [Presentation] ビンパッキング問題 (2015)
  • Author(s): 藤原 洋志
  • Organizer: 日本オペレーションズ・リサーチ学会中部支部講演会
  • Place of Presentation: 愛知県立大学サテライトキャンパス
  • Year and Date: 2015-12-19
  • Invited
• [Presentation] An Algorithm for the Huffman Tree Problem with Unit Step Functions (2015)
  • Author(s): Hiroshi Fujiwara, Takuya Nakamura, and Toshihiro Fujito
  • Organizer: The 8th Annual Meeting of Asian Association for Algorithms and Computation (AAAC2015)
  • Place of Presentation: 安芸グランドホテル（広島県廿日市市）
  • Year and Date: 2015-05-09
  • Int'l Joint Research
• [Presentation] 円周n等分点への質点配置問題 (2015)
  • Author(s): 藤原 洋志
  • Organizer: 列挙アルゴリズムセミナー
  • Place of Presentation: 群馬大学 伊香保研修所
  • Year and Date: 2015-03-05 – 2015-03-07
• [Presentation] 円周n等分点への質点配置問題 (2015)
  • Author(s): 藤原 洋志
  • Organizer: グレブナー若手集会
  • Place of Presentation: 信州大学 松本キャンパス
  • Year and Date: 2015-01-31 – 2015-02-02
• [Presentation] Online Weight Balancing on the Unit Circle (2013)
  • Author(s): Hiroshi Fujiwara, Takahiro Seki, and Toshihiro Fujito
  • Organizer: The 16th Japan Conference on Discrete and Computational Geometry and Graphs (JCDCGG2013)
  • Place of Presentation: 東京理科大
• [Presentation] Lower Bounds for the Multislope Ski-Rental Problem (2013)
  • Author(s): Hiroshi Fujiwara, Yasuhiro Konno, and Toshihiro Fujito
  • Organizer: The 11th International Symposium on Operations Research and its Applications (ISORA2013)
  • Place of Presentation: 中国、安徽省、黄山
• [Presentation] Improved Lower Bounds for the Bin Packing Problem with Cardinality Constraints (2013)
  • Author(s): Hiroshi Fujiwara and Koji Kobayashi
  • Organizer: 夏のLAシンポジウム
  • Place of Presentation: 休暇村志賀島
• [Presentation] Improved Lower Bounds for the Online Bin Packing Problem with Cardinality Constraints (2013)
  • Author(s): Hiroshi Fujiwara and Koji Kobayashi
  • Organizer: The 19th Annual International Computing and Combinatorics Conference (COCOON2013)
  • Place of Presentation: 中国、杭州、浙江大学
• [Presentation] スキーレンタル問題とオンライン最適化 (2013)
  • Author(s): 藤原 洋志
  • Organizer: 「文部科学省委託事業 数学協働プログラム」 最適化ワークショップ: 拡がっていく最適化
  • Place of Presentation: 九州大学伊都キャンパス マス・フォア・インダストリ研究所
  • Invited
• [Presentation] 携帯パケット通信料問題に対するオンラインアルゴリズム (2012)
  • Author(s): 松田 淳志, 藤原 洋志, 藤戸 敏弘
  • Organizer: 電気関係学会東海支部連合大会
  • Place of Presentation: 豊橋技術科学大学
• [Presentation] On the Best Possible Competitive Ratio for Multislope Ski Rental (2012)
  • Author(s): Hiroshi Fujiwara
  • Organizer: 電子科技大学計算機学院学者論壇
  • Place of Presentation: 中国、成都、電子科技大学
  • Invited
• [Presentation] Solving the Infinite-Slope Ski Rental via Functional Analysis (2012)
  • Author(s): Hiroshi Fujiwara
  • Organizer: The 5th Annual Meeting of the Asian Association for Algorithms and Computation (AAAC2012)
  • Place of Presentation: 中国、上海、復旦大学
• [Presentation] On the Best Possible Competitive Ratio for Multislope Ski Rental (2012)
  • Author(s): Hiroshi Fujiwara, Takuma Kitano, and Toshihiro Fujito
  • Organizer: The 22nd International Symposium on Algorithms and Computation (ISAAC2011)
  • Place of Presentation: ワークピア横浜
• [Presentation] 円周上へのアイテム配置問題 (2012)
  • Author(s): 藤原 洋志
  • Organizer: 列挙アルゴリズムセミナー
  • Place of Presentation: 群馬大学伊香保研修所
• [Presentation] 関数最適化に基づくアルゴリズムの性能解析 (2011)
  • Author(s): 藤原 洋志, 関口 良行
  • Organizer: 夏のLAシンポジウム
  • Place of Presentation: ザヴィラ浜名湖
• [Presentation] 携帯パケット通信料問題に対するオンラインアルゴリズム (2011)
  • Author(s): 松田 淳志, 藤原 洋志, 藤戸 敏弘
  • Organizer: 夏のLAシンポジウム
  • Place of Presentation: ザヴィラ浜名湖
• [Presentation] 単位円周上におけるアイテム配置問題 (2011)
  • Author(s): 関 孝洋, 藤原 洋志, 藤戸 敏弘
  • Organizer: 夏のLAシンポジウム
  • Place of Presentation: ザヴィラ浜名湖
• [Book] Encyclopedia of Algorithms (2015)
  • Author(s): Hiroshi Fujiwara and Koji M. Kobayashi
  • Publisher: Springer
• [Book] Python言語によるプログラミングイントロダクション: 世界標準MIT教科書 (2014)
  • Author(s): John V. Guttag (原著), 久保 幹雄 (監修, 翻訳), 麻生 敏正 (翻訳), 木村 泰紀 (翻訳), 小林 和博 (翻訳), 関口 良行 (翻訳), 並木 誠 (翻訳), 藤原 洋志 (翻訳)
  • Total Pages: 323
  • Publisher: 近代科学社