# Order-preserving pattern matching indeterminate strings

Rui Henriques, Alexandre P. Francisco, Luís M.S. Russo, Hideo Bannai

## 抄録

Given an indeterminate string pattern p and an indeterminate string text t, the problem of orderpreserving pattern matching with character uncertainties (μOPPM) is to find all substrings of t that satisfy one of the possible orderings defined by p. When the text and pattern are determinate strings, we are in the presence of the well-studied exact order-preserving pattern matching (OPPM) problem with diverse applications on time series analysis. Despite its relevance, the exact OPPM problem suffers from two major drawbacks: 1) the inability to deal with indetermination in the text, thus preventing the analysis of noisy time series; and 2) the inability to deal with indetermination in the pattern, thus imposing the strict satisfaction of the orders among all pattern positions. In this paper, we provide the first polynomial algorithms to answer the μOPPM problem when: 1) indetermination is observed on the pattern or text; and 2) indetermination is observed on both the pattern and the text and given by uncertainties between pairs of characters. First, given two strings with the same length m and O(r) uncertain characters per string position, we show that the μOPPM problem can be solved in O(mr lg r) time when one string is indeterminate and r ∈ N+ and in O(m2) time when both strings are indeterminate and r=2. Second, given an indeterminate text string of length n, we show that μOPPM can be efficiently solved in polynomial time and linear space.

本文言語 英語 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 Binhai Zhu, Gonzalo Navarro, David Sankoff Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing 21-215 195 9783959770743 https://doi.org/10.4230/LIPIcs.CPM.2018.2 出版済み - 5 1 2018 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 - Qingdao, 中国継続期間: 7 2 2018 → 7 4 2018

### 出版物シリーズ

名前 Leibniz International Proceedings in Informatics, LIPIcs 105 1868-8969

### その他

その他 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 中国 Qingdao 7/2/18 → 7/4/18

• ソフトウェア

## フィンガープリント

「Order-preserving pattern matching indeterminate strings」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。