### Abstract

We analyze the complexity of graph reachability queries on ST-graphs, defined as directed acyclic graphs (DAGs) obtained by merging the suffix tree of a given string and its suffix links. Using a simplified reachability labeling algorithm presented by Agrawal et al. (1989), we show that for a random string of length n, its ST-graph can be preprocessed in O(n log n) expected time and space to answer reachability queries in O(log n) time. Furthermore, we present a series of strings that require Θ(n√n) time and space to answer reachability queries in O(log n) time for the same algorithm. Exhaustive computational calculations for strings of length n ≤ 33 have revealed that the same strings are also the worst case instances of the algorithm. We therefore conjecture that reachability queries can be answered in O(log n) time with a worst case time and space preprocessing complexity of Θ(n√n).

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

Pages | 212-225 |

Number of pages | 14 |

Publication status | Published - Dec 1 2006 |

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

### Publication series

Name | Proceedings of the Prague Stringology Conference '06 |
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### 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. 212-225). (Proceedings of the Prague Stringology Conference '06).

**Reachability on suffix tree graphs.** / Higa, Yasuto; Bannai, Hideo; Inenaga, Shunsuke; Takeda, Masayuki.

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

*Proceedings of the Prague Stringology Conference '06.*Proceedings of the Prague Stringology Conference '06, pp. 212-225, Prague Stringology Conference '06, PSC 2006, Prague, Czech Republic, 8/28/06.

}

TY - GEN

T1 - Reachability on suffix tree graphs

AU - Higa, Yasuto

AU - Bannai, Hideo

AU - Inenaga, Shunsuke

AU - Takeda, Masayuki

PY - 2006/12/1

Y1 - 2006/12/1

N2 - We analyze the complexity of graph reachability queries on ST-graphs, defined as directed acyclic graphs (DAGs) obtained by merging the suffix tree of a given string and its suffix links. Using a simplified reachability labeling algorithm presented by Agrawal et al. (1989), we show that for a random string of length n, its ST-graph can be preprocessed in O(n log n) expected time and space to answer reachability queries in O(log n) time. Furthermore, we present a series of strings that require Θ(n√n) time and space to answer reachability queries in O(log n) time for the same algorithm. Exhaustive computational calculations for strings of length n ≤ 33 have revealed that the same strings are also the worst case instances of the algorithm. We therefore conjecture that reachability queries can be answered in O(log n) time with a worst case time and space preprocessing complexity of Θ(n√n).

AB - We analyze the complexity of graph reachability queries on ST-graphs, defined as directed acyclic graphs (DAGs) obtained by merging the suffix tree of a given string and its suffix links. Using a simplified reachability labeling algorithm presented by Agrawal et al. (1989), we show that for a random string of length n, its ST-graph can be preprocessed in O(n log n) expected time and space to answer reachability queries in O(log n) time. Furthermore, we present a series of strings that require Θ(n√n) time and space to answer reachability queries in O(log n) time for the same algorithm. Exhaustive computational calculations for strings of length n ≤ 33 have revealed that the same strings are also the worst case instances of the algorithm. We therefore conjecture that reachability queries can be answered in O(log n) time with a worst case time and space preprocessing complexity of Θ(n√n).

UR - http://www.scopus.com/inward/record.url?scp=84869104160&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:84869104160

SN - 8001035336

SN - 9788001035337

T3 - Proceedings of the Prague Stringology Conference '06

SP - 212

EP - 225

BT - Proceedings of the Prague Stringology Conference '06

ER -