The parser has some similarities with the bidirectional parser of . They present a bidirectional parser in which analyses are also discovered from the anchor of a lexicalized tree outward.
An important difference with their approach lies within the way in which auxiliary trees are handled. In our case, an auxiliary tree is traversed from the (known) foot node, rather than from the anchor of the auxiliary tree. This is reflected by our requirement that the head-corner of an auxiliary tree is its foot node. In the parser of  the parser proceeds from the lexical anchor of an auxiliary tree. This implies that there is some non-determinism in the case of adjunction: the parser does not take into account the possible analysis of a foot node and jumps over a substring possibly dominated by the foot node.
Furthermore, the bidirectional parser of  proceeds bottom-up from the anchor of an elementary tree upward. However, subtrees of an elementary tree that do not lie on this path are recognized in a top-down fashion. In the head-corner parser such subtrees are also processed bottom-up, starting from the head-corner of this subtree.
Finally note that the head-corner parser deals with substitution, whereas  do not consider the possibility of substitution.