  Visibility graph (VG) transformation is a technique used to convert a time
series into a graph based on specific visibility criteria. It has attracted
increasing interest in the fields of time series analysis, forecasting, and
classification. Optimizing the VG transformation algorithm to accelerate the
process is a critical aspect of VG-related research, as it enhances the
applicability of VG transformation in latency-sensitive areas and conserves
computational resources. In the real world, many time series are presented in
the form of data streams. Despite the proposal of the concept of VG's online
functionality, previous studies have not thoroughly explored the acceleration
of VG transformation by leveraging the characteristics of data streams. In this
paper, we propose that an efficient online VG algorithm should adhere to two
criteria and develop a linear-time method, termed the LOT framework, for both
natural and horizontal visibility graph transformations in data stream
scenarios. Experiments are conducted on two datasets, comparing our approach
with five existing methods as baselines. The results demonstrate the validity
and promising computational efficiency of our framework.
