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In this paper, we propose a graph-based dependency parsing model using dynamic features. The dynamic features, which are derived from the partial tree during bottom-up chart parsing, play an important role in finding the correct heads. Based on the beneficial aspects of the head-final property of Korean, we suggest a variant of the CYK parsing algorithm with an O(n3) complexity which has the ability to search for the maximum spanning tree (MST) from all projective trees. Compared to Eisner's algorithm, this algorithm is time-efficient in parsing all other head-final languages. We also explain why the graph-based approaches are seldom attempted in parsing morphologically rich languages (MRLs) and suggest a morpheme-level dependency representation as a solution. Finally, we evaluate the proposed method on the KAIST corpus using two discriminative online learning methods (the averaged perceptron algorithm and passive-aggressive algorithm) and show that the trained parser achieves the best reported parsing accuracy. [ABSTRACT FROM AUTHOR]