\section{Related Work}\label{sec:related_work}

% Na literatura, os únicos trabalhos que empregam árvores de sufixo para analisar séries temporais são os descritos em~\cite{Lin2004}~e~\cite{Faraz2011}.
% No entanto, esses trabalhos diferem da nossa proposta pois enfocam, respectivamente, em mineração visual de séries temporais e em previsão de comportamento de séries (\textit{forecasting}).
% Adicionalmente, esses trabalhos não usam árvores de sufixo generalizadas, impossibilitando que diversas \textit{strings} sejam analisadas. 
% Essas diferenças com relação ao propósito e às funcionalidades oferecidas motivam o desenvolvimento de um novo método de acesso que permita a indexação de séries temporais por meio de árvores de sufixo generalizadas.


In the literature, there are few approaches that employ suffix trees for analyzing time series.
Lin et al. (2005)~\nocite{Lin2005} introduced the VizTree, a time series pattern discovery and visualization system based on suffix trees.
The proposed visualization approach works by transforming the time series into strings using SAX, and encoding these strings into a modified suffix tree with properties of patterns mapped onto colors and others visual properties.
% VizTree provides visual and interactive solutions to many pattern discovery problems.
%, including the discovery of frequently occurring patterns (motif discovery), surprising patterns (anomaly detection), and query by content.

In~\cite{Faraz2011}, it was proposed a noise resilient algorithm for periodicity detection using suffix trees as the basic data structure. 
The algorithm calculates symbols and segment periodicity and detects the partial periodicity in time series. 
The presented experiments have shown that their proposal performs more efficiently when compared to other algorithms in presence of noise.
That is, when noise was added, mixed or even withdrawn, the algorithm did not suffer from such conditions. 

However, the aforementioned approaches differ from our work on their purpose and on the characteristics of the employed suffix tree.
In detail, they focus on time series visual mining and time series behavior forecasting, whereas our objective is to find time series similar to a given one.
Furthermore, they do not employ multi-scale data structures such as generalized suffix trees, making it too costly to analyze simultaneously more than one string.
Conversely, we use generalized suffix trees as a basis for our proposal.
These differences motivated the development of a new access method that allows indexing time series using generalized suffix trees.
