LZ77 using the suffix tree

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I have some problems understanding of how to effectively use the suffix tree in LZ77 with a sliding window, especially with deleting the suffix.

I seems that if I have the window of length m I need to always remove the suffixes with length greater than m, however the procedure can take O(m) to remove the whole suffix, so it takes a lot of time. Can anyone explain greater solution or give a useful link? Thanks in advance!

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