### 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 $Θ(n)$ 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 $Θ {n}$.

Original language | English |
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Pages (from-to) | 147-162 |

Number of pages | 16 |

Journal | International Journal of Foundations of Computer Science |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 1 2008 |

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### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)

### Cite this

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

Research output: Contribution to journal › Article

*International Journal of Foundations of Computer Science*, vol. 19, no. 1, pp. 147-162. https://doi.org/10.1142/S0129054108005590

}

TY - JOUR

T1 - Reachability on suffix tree graphs

AU - Higa, Yasuto

AU - Bannai, Hideo

AU - Inenaga, Shunsuke

AU - Takeda, Masayuki

PY - 2008/2/1

Y1 - 2008/2/1

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 $Θ(n)$ 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 $Θ {n}$.

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 $Θ(n)$ 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 $Θ {n}$.

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U2 - 10.1142/S0129054108005590

DO - 10.1142/S0129054108005590

M3 - Article

VL - 19

SP - 147

EP - 162

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 1

ER -