  Causal discovery studies the problem of mining causal relationships between
variables from data, which is of primary interest in science. During the past
decades, significant amount of progresses have been made toward this
fundamental data mining paradigm. Recent years, as the availability of abundant
large-sized and complex observational data, the constrain-based approaches have
gradually attracted a lot of interest and have been widely applied to many
diverse real-world problems due to the fast running speed and easy generalizing
to the problem of causal insufficiency. In this paper, we aim to review the
constraint-based causal discovery algorithms. Firstly, we discuss the learning
paradigm of the constraint-based approaches. Secondly and primarily, the
state-of-the-art constraint-based casual inference algorithms are surveyed with
the detailed analysis. Thirdly, several related open-source software packages
and benchmark data repositories are briefly summarized. As a conclusion, some
open problems in constraint-based causal discovery are outlined for future
research.
