TY - GEN

T1 - Fully dynamic data structure for LCE queries in compressed space

AU - Nishimoto, Takaaki

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2016/8/1

Y1 - 2016/8/1

N2 - A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z logN log∗M,N)) [Mehlhorn et al., Algorithmica 17(2):183- 198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(logN + log ℓ log∗M) time, where ℓ is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M ≥ 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(wfA) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + logN log∗M)fA) time, where fA = O(min{log log M log log w/log log log M, √log w/log log w}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(NfA) time from uncompressed string T; in O(n log log(n log∗M) logN log∗M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(zfA logN log∗M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.

AB - A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z logN log∗M,N)) [Mehlhorn et al., Algorithmica 17(2):183- 198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(logN + log ℓ log∗M) time, where ℓ is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M ≥ 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(wfA) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + logN log∗M)fA) time, where fA = O(min{log log M log log w/log log log M, √log w/log log w}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(NfA) time from uncompressed string T; in O(n log log(n log∗M) logN log∗M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(zfA logN log∗M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.

UR - http://www.scopus.com/inward/record.url?scp=85012885943&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012885943&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2016.72

DO - 10.4230/LIPIcs.MFCS.2016.72

M3 - Conference contribution

AN - SCOPUS:85012885943

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

A2 - Muscholl, Anca

A2 - Faliszewski, Piotr

A2 - Niedermeier, Rolf

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

Y2 - 22 August 2016 through 26 August 2016

ER -