### Abstract

The suffix tree of string w represents all suffixes of w, and thus it supports full indexing of w for exact pattern matching. On the other hand, a sparse suffix tree of w represents only a subset of the suffixes of w, and therefore it supports sparse indexing of w. There has been a wide range of applications of sparse suffix trees, e.g., natural language processing and biological sequence analysis. Word suffix trees are a variant of sparse suffix trees that are defined for strings that contain a special word delimiter #. Namely, the word suffix tree of string w = w _{1}w _{2} · · ·w _{k}, consisting of k words each ending with #, represents only the k suffixes of w of the form w _{i} · · ·w _{k}. Recently, we presented an algorithm which builds word suffix trees in O(n) time with O(k) space, where n is the length of w. In addition, we proposed sparse directed acyclic word graphs (SDAWGs) and an on-line algorithm for constructing them, working in O(n) time and space. As a further achievement of this research direction, this paper introduces yet a new text indexing structure named sparse compact directed acyclic word graphs (SCDAWGs). We show that the size of SCDAWGs is smaller than that of word suffix trees and SDAWGs, and present an SCDAWG construction algorithm that works in O(n) time with O(k) space and in an on-line manner.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference '06 |

Pages | 197-211 |

Number of pages | 15 |

Publication status | Published - 2006 |

Event | Prague Stringology Conference '06, PSC 2006 - Prague, Czech Republic Duration: Aug 28 2006 → Aug 30 2006 |

### Other

Other | Prague Stringology Conference '06, PSC 2006 |
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Country | Czech Republic |

City | Prague |

Period | 8/28/06 → 8/30/06 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Prague Stringology Conference '06*(pp. 197-211)

**Sparse compact directed acyclic word graphs.** / Inenaga, Shunsuke; Takeda, Masayuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Prague Stringology Conference '06.*pp. 197-211, Prague Stringology Conference '06, PSC 2006, Prague, Czech Republic, 8/28/06.

}

TY - GEN

T1 - Sparse compact directed acyclic word graphs

AU - Inenaga, Shunsuke

AU - Takeda, Masayuki

PY - 2006

Y1 - 2006

N2 - The suffix tree of string w represents all suffixes of w, and thus it supports full indexing of w for exact pattern matching. On the other hand, a sparse suffix tree of w represents only a subset of the suffixes of w, and therefore it supports sparse indexing of w. There has been a wide range of applications of sparse suffix trees, e.g., natural language processing and biological sequence analysis. Word suffix trees are a variant of sparse suffix trees that are defined for strings that contain a special word delimiter #. Namely, the word suffix tree of string w = w 1w 2 · · ·w k, consisting of k words each ending with #, represents only the k suffixes of w of the form w i · · ·w k. Recently, we presented an algorithm which builds word suffix trees in O(n) time with O(k) space, where n is the length of w. In addition, we proposed sparse directed acyclic word graphs (SDAWGs) and an on-line algorithm for constructing them, working in O(n) time and space. As a further achievement of this research direction, this paper introduces yet a new text indexing structure named sparse compact directed acyclic word graphs (SCDAWGs). We show that the size of SCDAWGs is smaller than that of word suffix trees and SDAWGs, and present an SCDAWG construction algorithm that works in O(n) time with O(k) space and in an on-line manner.

AB - The suffix tree of string w represents all suffixes of w, and thus it supports full indexing of w for exact pattern matching. On the other hand, a sparse suffix tree of w represents only a subset of the suffixes of w, and therefore it supports sparse indexing of w. There has been a wide range of applications of sparse suffix trees, e.g., natural language processing and biological sequence analysis. Word suffix trees are a variant of sparse suffix trees that are defined for strings that contain a special word delimiter #. Namely, the word suffix tree of string w = w 1w 2 · · ·w k, consisting of k words each ending with #, represents only the k suffixes of w of the form w i · · ·w k. Recently, we presented an algorithm which builds word suffix trees in O(n) time with O(k) space, where n is the length of w. In addition, we proposed sparse directed acyclic word graphs (SDAWGs) and an on-line algorithm for constructing them, working in O(n) time and space. As a further achievement of this research direction, this paper introduces yet a new text indexing structure named sparse compact directed acyclic word graphs (SCDAWGs). We show that the size of SCDAWGs is smaller than that of word suffix trees and SDAWGs, and present an SCDAWG construction algorithm that works in O(n) time with O(k) space and in an on-line manner.

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UR - http://www.scopus.com/inward/citedby.url?scp=37849020017&partnerID=8YFLogxK

M3 - Conference contribution

SN - 8001035336

SN - 9788001035337

SP - 197

EP - 211

BT - Proceedings of the Prague Stringology Conference '06

ER -