Reachability on suffix tree graphs

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)147-162
Number of pages16
JournalInternational Journal of Foundations of Computer Science
Volume19
Issue number1
DOIs
Publication statusPublished - Feb 1 2008

Fingerprint

Merging
Labeling

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

Cite this

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

In: International Journal of Foundations of Computer Science, Vol. 19, No. 1, 01.02.2008, p. 147-162.

Research output: Contribution to journalArticle

@article{b7acde63e4114a9987315c0dd2dbadba,
title = "Reachability on suffix tree graphs",
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 $Θ {n}$.",
author = "Yasuto Higa and Hideo Bannai and Shunsuke Inenaga and Masayuki Takeda",
year = "2008",
month = "2",
day = "1",
doi = "10.1142/S0129054108005590",
language = "English",
volume = "19",
pages = "147--162",
journal = "International Journal of Foundations of Computer Science",
issn = "0129-0541",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

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 $Θ {n}$.

UR - http://www.scopus.com/inward/record.url?scp=43949113286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949113286&partnerID=8YFLogxK

U2 - 10.1142/S0129054108005590

DO - 10.1142/S0129054108005590

M3 - Article

AN - SCOPUS:43949113286

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 -