Given a text T and a pattern P over alphabet Σ, the classic exact
matching problem searches for all occurrences of pattern P in text T.
Unlike exact matching problem, order-preserving pattern matching (OPPM)
considers the relative order of elements, rather than their real values. In
this paper, we propose an efficient algorithm for OPPM problem using the
"duel-and-sweep" paradigm. Our algorithm runs in O(n+mlogm) time in
general and O(n+m) time under an assumption that the characters in a string
can be sorted in linear time with respect to the string size. We also perform
experiments and show that our algorithm is faster that KMP-based algorithm.
Last, we introduce the two-dimensional order preserved pattern matching and
give a duel and sweep algorithm that runs in O(n2) time for duel stage and
O(n2m) time for sweeping time with O(m3) preprocessing time.Comment: 13 pages, 5 figure