TY - GEN

T1 - Linear-size CDAWG

T2 - 24th International Symposium on String Processing and Information Retrieval, SPIRE 2017

AU - Takagi, Takuya

AU - Goto, Keisuke

AU - Fujishige, Yuta

AU - Inenaga, Shunsuke

AU - Arimura, Hiroki

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - In this paper, we propose a novel approach to combine compact directed acyclic word graphs (CDAWGs) and grammar-based compression. This leads us to an efficient self-index, called Linear-size CDAWGs (L-CDAWGs), which can be represented with O(ẽT log n) bits of space allowing for O(log n) -time random and O(1)-time sequential accesses to edge labels, and O(m log σ + occ) -time pattern matching. Here, ẽT is the number of all extensions of maximal repeats in T, n and m are respectively the lengths of the text T and a given pattern, σ is the alphabet size, and occ is the number of occurrences of the pattern in T. The repetitiveness measure ẽT is known to be much smaller than the text length n for highly repetitive text. For constant alphabets, our L-CDAWGs achieve O(m + occ ) pattern matching time with O(eTr log n) bits of space, which improves the pattern matching time of Belazzougui et al.’s run-length BWT-CDAWGs by a factor of log log n, with the same space complexity. Here, eTr is the number of right extensions of maximal repeats in T. As a byproduct, our result gives a way of constructing a straight-line program (SLP) of size O(ẽT) for a given text T in O(n + ẽT log σ) time.

AB - In this paper, we propose a novel approach to combine compact directed acyclic word graphs (CDAWGs) and grammar-based compression. This leads us to an efficient self-index, called Linear-size CDAWGs (L-CDAWGs), which can be represented with O(ẽT log n) bits of space allowing for O(log n) -time random and O(1)-time sequential accesses to edge labels, and O(m log σ + occ) -time pattern matching. Here, ẽT is the number of all extensions of maximal repeats in T, n and m are respectively the lengths of the text T and a given pattern, σ is the alphabet size, and occ is the number of occurrences of the pattern in T. The repetitiveness measure ẽT is known to be much smaller than the text length n for highly repetitive text. For constant alphabets, our L-CDAWGs achieve O(m + occ ) pattern matching time with O(eTr log n) bits of space, which improves the pattern matching time of Belazzougui et al.’s run-length BWT-CDAWGs by a factor of log log n, with the same space complexity. Here, eTr is the number of right extensions of maximal repeats in T. As a byproduct, our result gives a way of constructing a straight-line program (SLP) of size O(ẽT) for a given text T in O(n + ẽT log σ) time.

UR - http://www.scopus.com/inward/record.url?scp=85030173354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030173354&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-67428-5_26

DO - 10.1007/978-3-319-67428-5_26

M3 - Conference contribution

AN - SCOPUS:85030173354

SN - 9783319674278

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 304

EP - 316

BT - String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings

A2 - Venturini, Rossano

A2 - Fici, Gabriele

A2 - Sciortino, Marinella

PB - Springer Verlag

Y2 - 25 September 2017 through 28 September 2017

ER -