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

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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UR - http://www.scopus.com/inward/citedby.url?scp=84907858098&partnerID=8YFLogxK

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 -