In pursuing machine understanding of human language, highly accurate syntactic analysis is a crucial step. In this work, we focus on dependency grammar, which models syntax by encoding transparent predicate-argument structures. Recent advances in dependency parsing have shown that employing higher-order subtree structures in graph-based parsers can substantially improve the parsing accuracy. However, the inefficiency of this approach increases with the order of the subtrees. This work explores a new reranking approach for dependency parsing that can utilize complex subtree representations by applying efficient subtree selection methods. We demonstrate the effectiveness of the approach in experiments conducted on the Penn Treebank and the Chinese Treebank. Our system achieves the best performance among known supervised systems evaluated on these datasets, improving the baseline accuracy from 91.88% to 93.42% for English, and from 87.39% to 89.25% for Chinese.