Fast Order-Preserving Pattern Matching

On Representations of Ternary Order Relations in Numeric Strings

“…The prefix representation has an ambiguity between di↵erent strings in ternary order relations [1]. For example, when x = (10, 30, 20), and y = (10, 20, 20), the prefix representations of both x and y are (1, 2, 2).…”

“…Cho et al [1] presented a modified match condition in ternary order relations, which can produce an O(n + m log m) algorithm as in binary order relations.…”

“…): Proceedings of the 2nd International Conference on Algorithms for Big Data, Palermo, Italy, 7-9 April 2014, published at http://ceur-ws.org/ of rank values (which they called the natural representation). Recently, variants of order-preserving matching have been studied such as order-preserving su x trees [2], approximate matching with k mismatches [3], and a Boyer-Moore type algorithm [1].…”

“…Kim et al [5] considered only binary order relations by assuming that all the characters in a string are distinct, while Kubica et al [7] considered ternary order relations but their match condition on equal characters was faulty and it was fixed later by Cho et al [1]. As there was no integrated study on the relationship between the representations of order relations, previous works [1,2,3] individually handled the cumbersome details of ternary order relations on their own works.…”

“…The order relation between two characters is a ternary relation (>, <, =) rather than a binary relation (>, <), but it was not su ciently studied in previous works [5,7,1]. In this paper, we extend the representations of order relations by Kim et al…”