As explained in Section 3.3.2, however, this can be implemented in constant time if the SINGLE-HEAD constraint is present by keeping track of the undirected connected component of each node in the generated dependency graph.
as explained in Section 2.3, the complexity of the planar parser with beam search is O(n), both for the unrestricted version and for the variant that enforces the SINGLE-HEAD and ACYCLICITY constraints.