文字列の辞書式順序の組合せ論とその応用

• Project/Area Number: 20H04141
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: Tokyo Medical and Dental University
• Principal Investigator: 坂内 英夫 東京医科歯科大学, M&Dデータ科学センター, 教授 (20323644)
• Co-Investigator(Kenkyū-buntansha): 井 智弘 九州工業大学, 大学院情報工学研究院, 准教授 (20773360) ; 関 新之助 電気通信大学, 大学院情報理工学研究科, 准教授 (30624944) ; 稲永 俊介 九州大学, システム情報科学研究院, 准教授 (60448404)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Project Status: Granted (Fiscal Year 2023)
• Budget Amount: ¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000); Fiscal Year 2023: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2022: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2021: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2020: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
• Keywords: 辞書式順序 / 繰り返し構造 / BWT / Lyndon語 / Lyndon 語 / 辞書式圧縮 / 双方向マクロスキーム / 文字列アトラクタ / 直線的プログラム / 全単射 BWT / Thue-Morse 文字列 / 繰り返し指標 / Lyndon 木 / 原始平方

Outline of Research at the Start

近年，情報通信・計測機器の発達により，多岐にわたる分野で膨大な量の文字列データが生み出され，利用可能となっている．このような大規模な文字列データを効率的に処理・解析する技術は多様な応用があるため広く必要とされ，極めて重要である．多様な文字列データに対して有効かつ効率的な処理・解析アルゴリズムを開発するには，文字列の様々な特徴に関する理論的・組合せ的性質の深い理解が必要不可欠である．本研究は，文字列の辞書式順序に着目し，その組合せ的性質の解明およびそれらを利用した効率的な文字列処理のアルゴリズムを開発を目指す．

Outline of Annual Research Achievements

本年度の主な成果は以下のとおりである。1) 文字列に部分列として含まれる最長の Lyndon 語を求める O(n^3) 時間・O(n) 領域のアルゴリズムを提案した。また、文字列の各接頭辞に対して順にこれを計算するオンラインな設定において、O(n^3σ) 時間・領域のアルゴリズムを提案した。ここで、σ はアルファベットサイズである。また、更に問題を拡張し、二つの文字列に共通して部分列として含まれる最長の Lyndon 語を計算する O(n^4σ) 時間・O(n^3) 領域のアルゴリズムを示した。これらの成果は国際会議 33rd International Workshop on Combinatorial Algorithms (IWOCA 2022) にて発表し、ベストペーパー賞を受賞した。2) 辞書式圧縮に関連する文字列の圧縮性指標のうち、計算が NP-困難であることが知られている最小文字列アトラクタのサイズ γ、最小双方向マクロスキームのサイズ b、及び最小の直線的プログラム（Straight Line Program)のサイズ g それぞれについて、MAX-SAT 問題に帰着し、MAX-SAT ソルバを利用することで、ある程度大きな文字列についても現実的な時間で厳密な値が計算できることを示し、これらの値を計算する初めての非自明な実装を提案した。また、この実装を利用することで γ の圧縮感度の下界を 2 から 2.5 に改善する文字列のクラスを発見した。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

コロナ禍においても徐々に出張ができるようになり、対面でのディスカッション等で共同研究に取り組めるようになって来ている。取り組んだ課題で良い成果が得られており、順調と考えられる。

Strategy for Future Research Activity

引き続き課題として挙げている問題に取り組むとともに、新しい課題についても適宜開拓してく。

Research Products

• [Int'l Joint Research] University of California, Berkeley(米国)
• [Int'l Joint Research] Helsinki University(フィンランド)
• [Int'l Joint Research] ヘルシンキ大学(フィンランド)
• [Int'l Joint Research] ニコラウス・コペルニクス大学(ポーランド)
• [Journal Article] Space-Efficient STR-IC-LCS Computation (2023)
  • Author(s): Yuuki Yonemoto, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai
  • Journal Title: Lecture Notes in Computer Science Volume: 13878 Pages: 372-384
  • DOI: 10.1007/978-3-031-23101-8_25
  • ISBN: 9783031231001, 9783031231018
  • Peer Reviewed
• [Journal Article] Online Algorithms for Finding Distinct Substrings with Length and Multiple Prefix and Suffix Conditions (2022)
  • Author(s): Leonard Laurentius、Inenaga Shunsuke、Bannai Hideo、Mieno Takuya
  • Journal Title: Proceedings of the 29th International Symposium on String Processing and Information Retrieval (SPIRE 2022) Volume: LNCS 13617 Pages: 24-37
  • DOI: 10.1007/978-3-031-20643-6_3
  • ISBN: 9783031206429, 9783031206436
  • Peer Reviewed
• [Journal Article] Computing Longest (Common) Lyndon Subsequences (2022)
  • Author(s): Hideo Bannai, Tomohiro I, Tomasz Kociumaka, Dominik Koeppl, Simon J. Puglisi
  • Journal Title: Proc. 33rd International Workshop on Combinatorial Algorithms (IWOCA) 2022 Volume: － Pages: 128-142
  • DOI: 10.1007/978-3-031-06678-8_10
  • ISBN: 9783031066771, 9783031066788
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Computing NP-Hard Repetitiveness Measures via MAX-SAT (2022)
  • Author(s): Bannai, Hideo、Goto, Keisuke、Ishihata, Masakazu、Kanda, Shunsuke、Koeppl, Dominik、Nishimoto, Takaaki
  • Journal Title: Proceedings of the 30th Annual European Symposium on Algorithms (ESA 2022) Volume: LIPIcs 244
  • Peer Reviewed / Open Access
• [Journal Article] Parameterized DAWGs: Efficient constructions and bidirectional pattern searches (2022)
  • Author(s): Katsuhito Nakashima, Noriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, Hideo Bannai, Ayumi Shinohara, Masayuki Takeda
  • Journal Title: Theoretical Computer Science Volume: 933 Pages: 21-42
  • DOI: 10.1016/j.tcs.2022.09.008
  • Peer Reviewed
• [Journal Article] Combinatorics of minimal absent words for a sliding window (2022)
  • Author(s): Tooru Akagi, Yuki Kuhara, Takuya Mieno, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Theoretical Computer Science Volume: 927 Pages: 109-119
  • DOI: 10.1016/j.tcs.2022.06.002
  • Peer Reviewed
• [Journal Article] Factorizing Strings into Repetitions (2022)
  • Author(s): Hiroe Inoue, Yoshiaki Matsuoka, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Theory of Computing Systems Volume: 66 Issue: 2 Pages: 484-501
  • DOI: 10.1007/s00224-022-10070-3
  • Peer Reviewed
• [Journal Article] Order-preserving pattern matching indeterminate strings (2022)
  • Author(s): Russo Luis M.S.、Costa Diogo、Henriques Rui、Bannai Hideo、Francisco Alexandre P.
  • Journal Title: Information and Computation Volume: 289 Pages: 104924-104924
  • DOI: 10.1016/j.ic.2022.104924
  • Peer Reviewed
• [Journal Article] Palindromic trees for a sliding window and its applications (2022)
  • Author(s): Takuya Mieno, Kiichi Watanabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Information Processing Letters Volume: 173 Pages: 106174-106174
  • DOI: 10.1016/j.ipl.2021.106174
  • Peer Reviewed / Open Access
• [Journal Article] c-trie++: A dynamic trie tailored for fast prefix searches (2021)
  • Author(s): Kazuya Tsuruta, Dominik Koeppl, Shunsuke Kanda, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Information and Computation Volume: - Pages: 104794-104794
  • DOI: 10.1016/j.ic.2021.104794
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] The Parameterized Suffix Tray (2021)
  • Author(s): Noriki Fujisato, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of 12th International Conference on Algorithms and Complexity Volume: 12701 Pages: 258-270
  • DOI: 10.1007/978-3-030-75242-2_18
  • ISBN: 9783030752415, 9783030752422
  • Peer Reviewed
• [Journal Article] Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time (2021)
  • Author(s): Hideo Bannai, Juha Karkkainen, Dominik Koeppl, Marcin Piatkowski
  • Journal Title: Proceedings of the 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021) Volume: LIPIcs 191
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A Separation of $$\gamma $$ and b via Thue-Morse Words (2021)
  • Author(s): Bannai Hideo、Funakoshi Mitsuru、I Tomohiro、Koeppl Dominik、Mieno Takuya、Nishimoto Takaaki
  • Journal Title: Proceedings of the 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021) Volume: LNCS 12944 Pages: 167-178
  • DOI: 10.1007/978-3-030-86692-1_14
  • ISBN: 9783030866914, 9783030866921
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Longest Common Rollercoasters (2021)
  • Author(s): Kosuke Fujita, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of 28th International Symposium on String Processing and Information Retrieval Volume: 12944 Pages: 21-32
  • DOI: 10.1007/978-3-030-86692-1_3
  • ISBN: 9783030866914, 9783030866921
  • Peer Reviewed
• [Journal Article] Grammar Index by Induced Suffix Sorting (2021)
  • Author(s): Tooru Akagi, Dominik Koeppl, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of 28th International Symposium on String Processing and Information Retrieval Volume: 12944 Pages: 85-99
  • DOI: 10.1007/978-3-030-86692-1_8
  • ISBN: 9783030866914, 9783030866921
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Efficiently computing runs on a trie (2021)
  • Author(s): Ryo Sugahara, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Theoretical Computer Science Volume: 887 Pages: 143-151
  • DOI: 10.1016/j.tcs.2021.07.011
  • Peer Reviewed / Open Access
• [Journal Article] Computing Minimal Unique Substrings for a Sliding Window (2021)
  • Author(s): Takuya Mieno, Yuta Fujishige, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Algorithmica Volume: 84 Issue: 3 Pages: 670-693
  • DOI: 10.1007/s00453-021-00864-1
  • Peer Reviewed / Open Access
• [Journal Article] The Smallest Grammar Problem Revisited (2021)
  • Author(s): Hideo Bannai, Momoko Hirayama, Danny Hucke, Shunsuke Inenaga, Artur Jez, Markus Lohrey, Carl Philipp Reh
  • Journal Title: IEEE Transactions on Information Theory Volume: 67(1) Issue: 1 Pages: 317-328
  • DOI: 10.1109/tit.2020.3038147
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Computing longest palindromic substring after single-character or block-wise edits (2021)
  • Author(s): Funakoshi Mitsuru, Nakashima Yuto, Inenaga Shunsuke, Bannai Hideo, Takeda Masayuki
  • Journal Title: Theoretical Computer Science Volume: 859 Pages: 116-133
  • DOI: 10.1016/j.tcs.2021.01.014
  • Peer Reviewed
• [Journal Article] Fast Algorithms for the Shortest Unique Palindromic Substring Problem on Run-Length Encoded Strings (2020)
  • Author(s): Watanabe Kiichi, Nakashima Yuto, Inenaga Shunsuke, Bannai Hideo, Takeda Masayuki
  • Journal Title: Theory of Computing Systems Volume: 64 Issue: 7 Pages: 1273-1291
  • DOI: 10.1007/s00224-020-09980-x
  • Peer Reviewed
• [Journal Article] DAWGs for Parameterized Matching: Online Construction and Related Indexing Structures (2020)
  • Author(s): Katsuhito Nakashima, Moriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, Hideo Bannai, Ayumi Shinohara, Masayuki Takeda
  • Journal Title: Proceedings of the 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020) Volume: LIPIcs 161
  • Peer Reviewed / Open Access
• [Journal Article] Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences (2020)
  • Author(s): Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Ayumi Shinohara
  • Journal Title: Proceedings of the 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020) Volume: LIPIcs 161
  • Peer Reviewed / Open Access
• [Journal Article] Grammar-compressed Self-index with Lyndon Words (2020)
  • Author(s): Kazuya Tsuruta, Dominik Koeppl, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: 情報処理学会論文誌数理モデル化と応用（TOM） Volume: 13(2) Pages: 84-92
  • Peer Reviewed
• [Journal Article] More Time-Space Tradeoffs for Finding a Shortest Unique Substring (2020)
  • Author(s): Hideo Bannai, Travis Gagie, Gary Hoppenworth, Simon J. Puglisi, Luis M. S. Russo
  • Journal Title: Algorithms Volume: 13(9) Issue: 9 Pages: 234-234
  • DOI: 10.3390/a13090234
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Lyndon Words, the Three Squares Lemma, and Primitive Squares (2020)
  • Author(s): Hideo Bannai, Takuya Mieno, Yuto Nakashima
  • Journal Title: Proceedings of 27th International Symposium on String Processing and Information Retrieval Volume: 12303 Pages: 265-273
  • DOI: 10.1007/978-3-030-59212-7_19
  • ISBN: 9783030592110, 9783030592127
  • Peer Reviewed
• [Journal Article] On repetitiveness measures of Thue-Morse words (2020)
  • Author(s): Kanaru Kutsukake, Takuya Matsumoto, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of 27th International Symposium on String Processing and Information Retrieval Volume: 12303 Pages: 213-220
  • DOI: 10.1007/978-3-030-59212-7_15
  • ISBN: 9783030592110, 9783030592127
  • Peer Reviewed
• [Journal Article] Longest Square Subsequence Problem Revisited (2020)
  • Author(s): Takafumi Inoue, Shunsuke Inenaga, Hideo Bannai
  • Journal Title: Proceedings of the 27th International Symposium on String Processing and Information Retrieval (SPIRE 2020) Volume: LNCS 12303 Pages: 147-154
  • DOI: 10.1007/978-3-030-59212-7_11
  • ISBN: 9783030592110, 9783030592127
  • Peer Reviewed
• [Journal Article] Towards Efficient Interactive Computation of Dynamic Time Warping Distance (2020)
  • Author(s): Akihiro Nishi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of 27th International Symposium on String Processing and Information Retrieval Volume: 12303 Pages: 27-41
  • DOI: 10.1007/978-3-030-59212-7_3
  • ISBN: 9783030592110, 9783030592127
  • Peer Reviewed
• [Journal Article] Space-efficient algorithms for computing minimal/shortest unique substrings (2020)
  • Author(s): Mieno Takuya, Koppl Dominik, Nakashima Yuto, Inenaga Shunsuke, Bannai Hideo, Takeda Masayuki
  • Journal Title: Theoretical Computer Science Volume: 845 Pages: 230-242
  • DOI: 10.1016/j.tcs.2020.09.017
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Compaction of Church Numerals (2019)
  • Author(s): Isamu Furuya, Takuya Kida
  • Journal Title: Algorithms Volume: 12(8) Issue: 4 Pages: 159-159
  • DOI: 10.3390/a13040103
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] Space-Efficient STR-IC-LCS Computation (2023)
  • Author(s): Yonemoto Yuuki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo
  • Organizer: 48th International Conference on Current Trends in Theory and Practice of Computere Science (SOFSEM 2023)
  • Int'l Joint Research
• [Presentation] Online Algorithms for Finding Distinct Substrings with Length and Multiple Prefix and Suffix Conditions (2022)
  • Author(s): Leonard Laurentius、Inenaga Shunsuke、Bannai Hideo、Mieno Takuya
  • Organizer: 29th International Symposium on String Processing and Information Retrieval (SPIRE 2022)
  • Int'l Joint Research
• [Presentation] Computing Longest (Common) Lyndon Subsequences (2022)
  • Author(s): Bannai Hideo、I Tomohiro、Kociumaka Tomasz、Koeppl Dominik、Puglisi Simon J.
  • Organizer: 33rd International Workshop on Combinatorial Algorithms (IWOCA 2022)
  • Int'l Joint Research
• [Presentation] Computing NP-Hard Repetitiveness Measures via MAX-SAT (2022)
  • Author(s): Bannai, Hideo、Goto, Keisuke、Ishihata, Masakazu、Kanda, Shunsuke、Koeppl, Dominik、Nishimoto, Takaaki
  • Organizer: 30th Annual European Symposium on Algorithms (ESA 2022)
  • Int'l Joint Research
• [Presentation] The Parameterized Suffix Tray (2021)
  • Author(s): Fujisato Noriki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 12th International Conference on Algorithms and Complexity (CIAC 2021)
  • Int'l Joint Research
• [Presentation] Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time (2021)
  • Author(s): Hideo Bannai, Juha Karkkainen, Dominik Koeppl, Marcin Piatkowski
  • Organizer: 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)
  • Int'l Joint Research
• [Presentation] Repetitions in Strings: A "Constant" Problem (2021)
  • Author(s): Hideo Bannai
  • Organizer: 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)
  • Int'l Joint Research / Invited
• [Presentation] A Separation of $$\gamma $$ and b via Thue-Morse Words (2021)
  • Author(s): Bannai Hideo、Funakoshi Mitsuru、I Tomohiro、Koeppl Dominik、Mieno Takuya、Nishimoto Takaaki
  • Organizer: 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021)
  • Int'l Joint Research
• [Presentation] Longest Common Rollercoasters (2021)
  • Author(s): Fujita Kosuke、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021)
  • Int'l Joint Research
• [Presentation] Grammar Index by Induced Suffix Sorting (2021)
  • Author(s): Akagi Tooru、Koeppl Dominik、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021)
  • Int'l Joint Research
• [Presentation] DAWGs for Parameterized Matching: Online Construction and Related Indexing Structures (2020)
  • Author(s): Katsuhito Nakashima, Moriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, Hideo Bannai, Ayumi Shinohara, Masayuki Takeda
  • Organizer: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
  • Int'l Joint Research
• [Presentation] Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences (2020)
  • Author(s): Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Ayumi Shinohara
  • Organizer: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
  • Int'l Joint Research
• [Presentation] Lyndon Words, the Three Squares Lemma, and Primitive Squares (2020)
  • Author(s): Hideo Bannai, Takuya Mieno, Yuto Nakashima
  • Organizer: 27th International Symposium on String Processing and Information Retrieval (SPIRE 2020)
  • Int'l Joint Research
• [Presentation] On Repetitiveness Measures of Thue-Morse Words (2020)
  • Author(s): Kanaru Kutsukake, Takuya Matsumoto, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: 27th International Symposium on String Processing and Information Retrieval (SPIRE 2020)
  • Int'l Joint Research
• [Presentation] Longest Square Subsequence Problem Revisited (2020)
  • Author(s): Takafumi Inoue, Shunsuke Inenaga, Hideo Bannai
  • Organizer: 27th International Symposium on String Processing and Information Retrieval (SPIRE 2020)
  • Int'l Joint Research
• [Presentation] Towards Efficient Interactive Computation of Dynamic Time Warping Distance (2020)
  • Author(s): Akihiro Nishi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: 27th International Symposium on String Processing and Information Retrieval (SPIRE 2020)
  • Int'l Joint Research
• [Remarks] MAX-SATソルバを利用してNP困難な圧縮性指標を計算するソフトウェア
  • URL: https://github.com/kg86/satcomp