TY - GEN
T1 - Faster compact on-line Lempel-ziv factorization
AU - Yamamoto, Jun'ichi
AU - I, Tomohiro
AU - Bannai, Hideo
AU - Inenaga, Shunsuke
AU - Takeda, Masayuki
N1 - Publisher Copyright:
© Jun'ichi Yamamoto, Tomohiro I, Hideo Bannai, Shunsuke Inenaga, and Masayuki Takeda.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2014/3/1
Y1 - 2014/3/1
N2 - We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in O(N logN) time and uses only O(N log σ) bits of working space, where N is the length of the string and σ is the size of the alphabet. This is a notable improvement compared to the performance of previous on-line algorithms using the same order of working space but running in either O(N log3N) time (Okanohara & Sadakane 2009) or O(N log2N) time (Starikovskaya 2012). The key to our new algorithm is in the utilization of an elegant but less popular index structure called Directed Acyclic Word Graphs, or DAWGs (Blumer et al. 1985). We also present an opportunistic variant of our algorithm, which, given the run length encoding of size m of a string of length N, computes the Lempel-Ziv factorization of the string on-line, in O (m · min{n (log logm)(log logN)/log log logN , √ logm/log logm o})time and O(mlogN) bits of space.
AB - We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in O(N logN) time and uses only O(N log σ) bits of working space, where N is the length of the string and σ is the size of the alphabet. This is a notable improvement compared to the performance of previous on-line algorithms using the same order of working space but running in either O(N log3N) time (Okanohara & Sadakane 2009) or O(N log2N) time (Starikovskaya 2012). The key to our new algorithm is in the utilization of an elegant but less popular index structure called Directed Acyclic Word Graphs, or DAWGs (Blumer et al. 1985). We also present an opportunistic variant of our algorithm, which, given the run length encoding of size m of a string of length N, computes the Lempel-Ziv factorization of the string on-line, in O (m · min{n (log logm)(log logN)/log log logN , √ logm/log logm o})time and O(mlogN) bits of space.
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U2 - 10.4230/LIPIcs.STACS.2014.675
DO - 10.4230/LIPIcs.STACS.2014.675
M3 - Conference contribution
AN - SCOPUS:84907858098
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 675
EP - 686
BT - 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014
A2 - Portier, Natacha
A2 - Mayr, Ernst W.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014
Y2 - 5 March 2014 through 8 March 2014
ER -