A fast and simple $O(z\log n)$-space index for finding approximately longest common substrings

We describe how, given a text $T[\mathrm{1..}n]$ and a positive constant $\epsilon$, we can build a simple $O(z\log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P[\mathrm{1..}m]$, in $O(m\log \log z+\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{g}(m+z))$ time and with high probability we can find a substring of $P$ that occurs in $T$ and whose length is at least a $(1-\epsilon )$-fraction of the length of a longest common substring of $P$ and $T$.