Approximating LZ77 in Small Space

Given a positive $ϵ\le 1$ and read-only access to a string (S [1…n]) whose LZ77 parse consists of $z$ phrases, with high probability we can build an LZ77-like parse of $S$ that consists of $\text{Oh}z\mathrm{/}ϵ$ phrases using $\text{Oh}{n}^{1+ϵ}$ time, $\text{Oh}{n}^{1+ϵ}\mathrm{/}B$ I/Os (where $B$ is the size of a disk block) and $\text{Oh}z\mathrm{/}ϵ$ space.