In this paper, we give a summary of various dependency chart parsing algorithms in terms of the use of parsing histories for a new dependency arc decision. Some parsing histories are closely related to the target dependency arc, and it is necessary for the parsing algorithm to take them into consideration. Each dependency treebank may have some unique characteristics, and it requires for the parser to model them by certain parsing histories. We show in experiments that proper selection of the parsing algorithm which reflect the dependency annotation of the coordinate structures improves the overall performance. 1