Reachability on suffix tree graphs

Yasuto Higa, Hideo Bannai, Shunsuke Inenaga, Masayuki Takeda

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

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

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