文字列の繰り返し構造の組合せ論と応用

2019 Fiscal Year Annual Research Report

• Project/Area Number: 16H02783
• Research Institution: Kyushu University
• Principal Investigator: 坂内 英夫 九州大学, システム情報科学研究院, 准教授 (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) ; 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): 2016-04-01 – 2020-03-31
• Keywords: トライ上の繰り返し構造 / 最長共通繰り返し構造 / 索引構造

Outline of Annual Research Achievements

本年度の主な成果は以下のとおりである 1) 辺に文字ラベルを持つ根付木(トライ）上に出現する極大繰り返し構造（連）を考え、辺数 n のトライに対して n 以下であることを示し、トライ上の連をすべて列挙する O(n (loglog n)^2) 時間アルゴリズムを提案した。また、トライ上の極大回文および異なる回文に関しても同様にそれぞれ 2n-1, n+1個以下dであることを示し、O(n log n) 時間ですべて列挙するアルゴリズムを提案した。2) 与えられた文字列の Lyndon 分解の項数 m と自己参照を許した LZ 分解の項数 z について、m < 4z という関係が成り立つことを示した。3) 前処理可能な文字列集合と、クエリ文字列が与えられたときに、クエリ文字列と文字列集合中の少なくとも k 個の文字列に共通な部分文字列のうち特定の性質をもつ最長のものを答える問題について、回分、平方、繰り返し構造、Lyndon語という性質について、線形時間の前処理で任意のクエリに対してクエリ長に線形時間で答えることのできるデータ構造とアルゴリズムを示した。4) パラメータ化接尾辞配列を直接構築する問題について、パラメータ化アルファベットのサイズがπ、静的アルファベットが整数アルファベットの時O(nπ) 時間、O(n) 領域で動作するアルゴリズムを示した。π が定数の時、これはパラメータ化接尾辞配列およびパラメータ化接尾辞木を構築する現時点で最速のアルゴリズムである。

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] ア・コルーニャ大学(スペイン)
  • Country Name: SPAIN
  • Counterpart Institution: ア・コルーニャ大学
• [Int'l Joint Research] ヘルシンキ大学(フィンランド)
  • Country Name: FINLAND
  • Counterpart Institution: ヘルシンキ大学
• [Journal Article] Refining the r-index (2020)
  • Author(s): Bannai Hideo、Gagie Travis、I Tomohiro
  • Journal Title: Theoretical Computer Science Volume: 812 Pages: 96～108
  • DOI: doi.org/10.1016/j.tcs.2019.08.005
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Dynamic index and LZ factorization in compressed space (2020)
  • Author(s): Nishimoto Takaaki、I Tomohiro、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Discrete Applied Mathematics Volume: 274 Pages: 116～129
  • DOI: doi.org/10.1016/j.dam.2019.01.014
  • Peer Reviewed
• [Journal Article] Finding all maximal perfect haplotype blocks in linear time (2020)
  • Author(s): Alanko Jarno、Bannai Hideo、Cazaux Bastien、Peterlongo Pierre、Stoye Jens
  • Journal Title: Algorithms for Molecular Biology Volume: 15 Pages: 2:1-7
  • DOI: doi.org/10.1186/s13015-020-0163-6
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Faster STR-EC-LCS Computation (2020)
  • Author(s): Yamada Kohei、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Proceedings of the 46th International Conference on Current Trends in Theory and Practice of Informatics (SOFSEM 2020) Volume: LNCS 12011 Pages: 125～135
  • DOI: 10.1007/978-3-030-38919-2_11
  • Peer Reviewed
• [Journal Article] Minimal Unique Substrings and Minimal Absent Words in a Sliding Window (2020)
  • Author(s): Mieno Takuya、Kuhara Yuki、Akagi Tooru、Fujishige Yuta、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Proceedings of the 46th International Conference on Current Trends in Theory and Practice of Informatics (SOFSEM 2020) Volume: LNCS 12011 Pages: 148～160
  • DOI: 10.1007/978-3-030-38919-2_13
  • Peer Reviewed
• [Journal Article] On the size of the smallest alphabet for Lyndon trees (2019)
  • Author(s): Nakashima Yuto、Takagi Takuya、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Theoretical Computer Science Volume: 792 Pages: 131～143
  • DOI: 10.1016/j.tcs.2018.06.044
  • Peer Reviewed
• [Journal Article] The Parameterized Position Heap of a Trie (2019)
  • Author(s): Fujisato Noriki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Proceedings of the 11th International Conference on Algorithms and Complexity (CIAC 2019) Volume: LNCS 11485 Pages: 237～248
  • DOI: 10.1007/978-3-030-17402-6_20
  • Peer Reviewed
• [Journal Article] Direct Linear Time Construction of Parameterized Suffix and LCP Arrays for Constant Alphabets (2019)
  • Author(s): Fujisato Noriki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Proceedings of the 26th International Symposium String Processing and Information Retrieval (SPIRE 2019) Volume: LNCS 11811 Pages: 382～391
  • DOI: 10.1007/978-3-030-32686-9_27
  • Peer Reviewed
• [Journal Article] On Longest Common Property Preserved Substring Queries (2019)
  • Author(s): Kai Kazuki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki、Kociumaka Tomasz
  • Journal Title: Proceedings of the 26th International Symposium String Processing and Information Retrieval (SPIRE 2019) Volume: LNCS 11811 Pages: 162～174
  • DOI: 10.1007/978-3-030-32686-9_12
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Compact Data Structures for Shortest Unique Substring Queries (2019)
  • Author(s): Mieno Takuya、Koeppl Dominik、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Proceedings of the 26th International Symposium String Processing and Information Retrieval (SPIRE 2019) Volume: LNCS 11811 Pages: 107～123
  • DOI: 10.1007/978-3-030-32686-9_8
  • Peer Reviewed
• [Journal Article] Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings (2019)
  • Author(s): Watanabe Kiichi、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Journal Title: Proceedings of the 30th Internal Workshop on Combinatorial Algorithms (IWOCA 2019) Volume: LNCS 11638 Pages: 430～441
  • DOI: 10.1007/978-3-030-25005-8_35
  • Peer Reviewed
• [Journal Article] An Improved Data Structure for Left-Right Maximal Generic Words Problem (2019)
  • Author(s): Yuta Fujishige, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of the 30th International Symposium on Algorithms and Computation (ISAAC 2019) Volume: LIPIcs 149 Pages: 40:1-40:12
  • DOI: 10.4230/LIPIcs.ISAAC.2019.40
  • Peer Reviewed / Open Access
• [Journal Article] On the Size of Overlapping Lempel-Ziv and Lyndon Factorizations (2019)
  • Author(s): Yuki Urabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of the 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) Volume: LIPIcs 128 Pages: 29:1-29:11
  • DOI: 10.4230/LIPIcs.CPM.2019.29
  • Peer Reviewed / Open Access
• [Journal Article] Faster Queries for Longest Substring Palindrome After Block Edit (2019)
  • Author(s): Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of the 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) Volume: LIPIcs 128 Pages: 27:1-27:13
  • DOI: 10.4230/LIPIcs.CPM.2019.27
  • Peer Reviewed / Open Access
• [Journal Article] Computing Runs on a Trie (2019)
  • Author(s): Ryo Sugahara, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of the 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) Volume: LIPIcs 128 Pages: 23:1-23:11
  • DOI: 10.4230/LIPIcs.CPM.2019.23
  • Peer Reviewed / Open Access
• [Journal Article] Indexing the Bijective BWT (2019)
  • Author(s): Hideo Bannai, Juha Karkkainen, Dominik Koeppl, Marcin Piatkowski
  • Journal Title: Proceedings of the 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) Volume: LIPIcs 128 Pages: 17:1-17:14
  • DOI: 10.4230/LIPIcs.CPM.2019.17
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] k-Abelian Pattern Matching: Revisited, Corrected, and Extended (2019)
  • Author(s): Golnaz Badkobeh, Hideo Bannai, Maxime Crochemore, Tomohiro I, Shunsuke Inenaga, Shiho Sugimoto
  • Journal Title: Proceedings of Prague Stringology Conference 2019 Volume: - Pages: 29-40
  • Peer Reviewed / Open Access
• [Journal Article] Computing Maximal Palindromes and Distinct Palindromes in a Trie (2019)
  • Author(s): Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Journal Title: Proceedings of Prague Stringology Conference 2019 Volume: - Pages: 3-15
  • Peer Reviewed / Open Access
• [Journal Article] Finding All Maximal Perfect Haplotype Blocks in Linear Time (2019)
  • Author(s): Jarno Alanko, Hideo Bannai, Bastien Cazaux, Pierre Peterlongo, Jens Stoye
  • Journal Title: Proceedings of the 19th International Workshop on Algorithms in Bioinformatics (WABI 2019) Volume: LIPIcs 143 Pages: 8:1-8:9
  • DOI: doi.org/10.4230/LIPIcs.WABI.2019.8
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] Faster STR-EC-LCS Computation (2020)
  • Author(s): Yamada Kohei、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 46th International Conference on Current Trends in Theory and Practice of Informatics (SOFSEM 2020)
  • Int'l Joint Research
• [Presentation] Minimal Unique Substrings and Minimal Absent Words in a Sliding Window (2020)
  • Author(s): Mieno Takuya、Kuhara Yuki、Akagi Tooru、Fujishige Yuta、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 46th International Conference on Current Trends in Theory and Practice of Informatics (SOFSEM 2020)
  • Int'l Joint Research
• [Presentation] The Parameterized Position Heap of a Trie (2019)
  • Author(s): Fujisato Noriki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 11th International Conference on Algorithms and Complexity (CIAC 2019)
  • Int'l Joint Research
• [Presentation] Direct Linear Time Construction of Parameterized Suffix and LCP Arrays for Constant Alphabets (2019)
  • Author(s): Fujisato Noriki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 26th International Symposium String Processing and Information Retrieval (SPIRE 2019)
  • Int'l Joint Research
• [Presentation] On Longest Common Property Preserved Substring Queries (2019)
  • Author(s): Kai Kazuki、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki、Kociumaka Tomasz
  • Organizer: 26th International Symposium String Processing and Information Retrieval (SPIRE 2019)
  • Int'l Joint Research
• [Presentation] Compact Data Structures for Shortest Unique Substring Queries (2019)
  • Author(s): Mieno Takuya、Koeppl Dominik、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 26th International Symposium String Processing and Information Retrieval (SPIRE 2019)
  • Int'l Joint Research
• [Presentation] Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings (2019)
  • Author(s): Watanabe Kiichi、Nakashima Yuto、Inenaga Shunsuke、Bannai Hideo、Takeda Masayuki
  • Organizer: 30th Internal Workshop on Combinatorial Algorithms (IWOCA 2019)
  • Int'l Joint Research
• [Presentation] On the Size of Overlapping Lempel-Ziv and Lyndon Factorizations (2019)
  • Author(s): Yuki Urabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
  • Int'l Joint Research
• [Presentation] Faster Queries for Longest Substring Palindrome After Block Edit (2019)
  • Author(s): Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
  • Int'l Joint Research
• [Presentation] Computing Runs on a Trie (2019)
  • Author(s): Ryo Sugahara, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
  • Int'l Joint Research
• [Presentation] Indexing the Bijective BWT (2019)
  • Author(s): Hideo Bannai, Juha Karkkainen, Dominik Koeppl, Marcin Piatkowski
  • Organizer: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
  • Int'l Joint Research
• [Presentation] k-Abelian Pattern Matching: Revisited, Corrected, and Extended (2019)
  • Author(s): Golnaz Badkobeh, Hideo Bannai, Maxime Crochemore, Tomohiro I, Shunsuke Inenaga, Shiho Sugimoto
  • Organizer: Prague Stringology Conference 2019
  • Int'l Joint Research
• [Presentation] Computing Maximal Palindromes and Distinct Palindromes in a Trie (2019)
  • Author(s): Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: Prague Stringology Conference 2019
  • Int'l Joint Research
• [Presentation] Finding All Maximal Perfect Haplotype Blocks in Linear Time (2019)
  • Author(s): Jarno Alanko, Hideo Bannai, Bastien Cazaux, Pierre Peterlongo, Jens Stoye
  • Organizer: 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)
  • Int'l Joint Research
• [Presentation] An Improved Data Structure for Left-Right Maximal Generic Words Problem (2019)
  • Author(s): Yuta Fujishige, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
  • Organizer: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
  • Int'l Joint Research