However, their model has a high order of time complexity , and thus cannot be applied in practice.

In this work, we develop a much faster model whose time complexity is linear in the number of sentences.

2The time complexity will be reduced to 0(M2n2), if we

greedy bottom-up strategy, we develop a discourse parser with a time complexity linear in the total number of sentences in the document.

Here we analyze the time complexity of each component in our discourse parser, to quantitatively demonstrate the time efficiency of our model.

overall time complexity to perform intra-sentential parsing is The reason is the following.

The time complexity for performing forward-backward inference on the single chain is 0((mk — i) x M2) = 0(mk — i), where the constant M is the size of the output vocabulary.

Due to the 0(n3) time complexity , where n is the number

8) have time complexity (9(n3) or — if we want to take the higher efficiency of computation for sparse graphs into account —(9(dn2) where n is the number of nodes and d the

If d < k, then the time complexity of CoSimRank is (9(k2n).

Thus, we have reduced SimRank’s cubic time complexity to a quadratic time complexity for CoSimRank or — assuming that the average degree d does not depend on n — SimRank’s quadratic time complexity to linear time complexity for the case of computing few similarities.

Unfortunately, SimRank has time complexity (9(n3) (where n is the number of nodes in the graph) and therefore does not scale to the large graphs that are typical of NLP.

Based on dependency structure, we are able to directly analyze the relations between the EDUs without worrying about the additional interior text spans, and apply the existing state-of-the-art dependency parsing techniques which have a relatively low time complexity .

It is well known that projective dependency parsing can be handled with the Eisner algorithm (1996) which is based on the bottom-up dynamic programming techniques with the time complexity of 0(n3).

(2005b), we adopt an efficient implementation of the Chu-Liu/Edmonds algorithm that is proposed by Tar-jan (1997) with O(n2) time complexity .

Third, to reduce the time complexity of the state-of-the-art constituency based parsing techniques, the approximate parsing approaches are prone to trap in local maximum.

We discuss the theoretical time complexity of looking up extraction patterns in a large corpus of

Figure 5: Time complexity of lookup operations for inputs of different sizes.

Time complexity of lookups.