Following (Joty et al., 2012), we implement a probabilistic CKY-like bottom-up algorithm for computing the most likely parse using dynamic programming.
with n discourse units, we use the upper-triangular portion of the n×n dynamic programming table D. Given U x (0) and U x (1) are the start and end EDU Ids of unit U x : where, k = argmax Note that, in contrast to previous studies on document-level parsing (Hernault et al., 2010;Subba and Di-Eugenio, 2009;Marcu, 2000b), which use a greedy algorithm, our approach finds a discourse tree that is globally optimal.