Reachability on suffix tree graphs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationProceedings of the Prague Stringology Conference '06
Pages212-225
Number of pages14
Publication statusPublished - Dec 1 2006
EventPrague Stringology Conference '06, PSC 2006 - Prague, Czech Republic
Duration: Aug 28 2006Aug 30 2006

Publication series

NameProceedings of the Prague Stringology Conference '06

Other

OtherPrague Stringology Conference '06, PSC 2006
CountryCzech Republic
CityPrague
Period8/28/068/30/06

Fingerprint

Suffix Tree
Reachability
Strings
Graph in graph theory
Query
Labeling Algorithm
Suffix
Directed Acyclic Graph
Merging
Preprocessing
Series

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Higa, Y., Bannai, H., Inenaga, S., & Takeda, M. (2006). Reachability on suffix tree graphs. In 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.

Proceedings of the Prague Stringology Conference '06. 2006. p. 212-225 (Proceedings of the Prague Stringology Conference '06).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Higa, Y, Bannai, H, Inenaga, S & Takeda, M 2006, Reachability on suffix tree graphs. in 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.
Higa Y, Bannai H, Inenaga S, Takeda M. Reachability on suffix tree graphs. In Proceedings of the Prague Stringology Conference '06. 2006. p. 212-225. (Proceedings of the Prague Stringology Conference '06).
Higa, Yasuto ; Bannai, Hideo ; Inenaga, Shunsuke ; Takeda, Masayuki. / Reachability on suffix tree graphs. Proceedings of the Prague Stringology Conference '06. 2006. pp. 212-225 (Proceedings of the Prague Stringology Conference '06).
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