The order preserving pattern matching (OPPM) problem is, given a pattern string p and a text string t, find all substrings of t which have the same relative orders as p. In this paper, we consider two variants of the OPPM problem where a set of text strings is given as a tree or a DAG. We show that the OPPM problem for a single pattern p of length m and a text tree T of size N can be solved in O(m+N) time with O(m) working space if the characters of p are drawn from an integer alphabet of polynomial size. The time complexity becomes O(m log m + N) if the pattern p is over a general ordered alphabet. We then show that the OPPM problem for a single pattern and a text DAG is NP-complete.
CITATION STYLE
Nakamura, T., Inenaga, S., Bannai, H., & Takeda, M. (2017). Order preserving pattern matching on trees and DAGs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10508 LNCS, pp. 271–277). Springer Verlag. https://doi.org/10.1007/978-3-319-67428-5_23
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