Converting SLP to LZ78 in almost Linear Time

Given a straight line program of size n, we are interested in constructing the LZ78 factorization of the corresponding text. We show how to perform such conversion in \(\mathcal{O}(n+m\log m)\) time, where m is the number of LZ78 codewords. This improves on the previously known \(\mathcal{O}(n\sqrt{N}+m\log N)\) solution [Bannai et al., SPIRE 2012]. The main tool in our algorithm is a data structure which allows us to efficiently operate on labels of the paths in a growing trie, and a certain method of recompressing the parse whenever it leads to decreasing its size.

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