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).

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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

T2 - Prague Stringology Conference '06, PSC 2006

Y2 - 28 August 2006 through 30 August 2006

ER -