TY - GEN

T1 - Order-preserving pattern matching indeterminate strings

AU - Henriques, Rui

AU - Francisco, Alexandre P.

AU - Russo, Luís M.S.

AU - Bannai, Hideo

N1 - Funding Information:
Funding This work was developed in the context of a secondment granted by the BIRDS MASC RISE project funded in part by EU H2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no.690941. This work was further supported by national funds through Fundação para a Ciência e Tecnologia (FCT) with reference UID/CEC/50021/2013.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

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U2 - 10.4230/LIPIcs.CPM.2018.2

DO - 10.4230/LIPIcs.CPM.2018.2

M3 - Conference contribution

AN - SCOPUS:85048250361

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 21

EP - 215

BT - 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018

A2 - Zhu, Binhai

A2 - Navarro, Gonzalo

A2 - Sankoff, David

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018

Y2 - 2 July 2018 through 4 July 2018

ER -