### 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 |

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)

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## Cite this

*International Journal of Foundations of Computer Science*,

*19*(1), 147-162. https://doi.org/10.1142/S0129054108005590