TY - GEN
T1 - Longest lyndon substring after edit
AU - Urabe, Yuki
AU - Nakashima, Yuto
AU - Inenaga, Shunsuke
AU - Bannai, Hideo
AU - Takeda, Masayuki
N1 - Publisher Copyright:
© 2018 Yoshifumi Sakai; licensed under Creative Commons License CC-BY.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T) denotes the length of the longest Lyndon substring of a string T. In this paper, we consider computing LLS(T′) where T′ is an edited string formed from T. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(log n) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of T is replaced by a given string of length l. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(l log σ + log n) time for any block edit where σ is the number of distinct characters in T. We can modify our algorithm so as to output all the longest Lyndon substrings of T′ for both problems.
AB - The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T) denotes the length of the longest Lyndon substring of a string T. In this paper, we consider computing LLS(T′) where T′ is an edited string formed from T. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(log n) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of T is replaced by a given string of length l. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(l log σ + log n) time for any block edit where σ is the number of distinct characters in T. We can modify our algorithm so as to output all the longest Lyndon substrings of T′ for both problems.
UR - https://www.scopus.com/pages/publications/85048299606
UR - https://www.scopus.com/pages/publications/85048299606#tab=citedBy
U2 - 10.4230/LIPIcs.CPM.2018.19
DO - 10.4230/LIPIcs.CPM.2018.19
M3 - Conference contribution
AN - SCOPUS:85048299606
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 191
EP - 1910
BT - 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018
A2 - Zhu, Binhai
A2 - Navarro, Gonzalo
A2 - Sankoff, David
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018
Y2 - 2 July 2018 through 4 July 2018
ER -