The languages in the CoNLL-2012 shared task represent a good variation of directionalities: Arabic is a consistently head-initial language; Chinese is a consistently head-final language; and English represents a language with mixed directionality since it places specifiers before the head and heavier constituents, such as prepositional phrases or relative clauses, after the syntactic head.
english is the most difficult case: it requires knowledge of the internal structure of the NP in order to correctly identify the head of a higher-order NP, which is non-trivial to capture in a heuristic or in rules.