The project page states that "trading off memory for running time, as implemented in tomato_miner.h, incurs at least one order of magnitude extra slowdown"
For instance, to look for a 42 cycle on a billion node graph, the reference algorithm uses 128MB.
If you want to get by with only 32MB, then you can run that alternative algorithm, but it will take about 128/32*25=100 times longer. The penalty factor of about 25 is due to losing the ability to represent edges with a single bit.
You can also parallelize by having more cores share the same memory but this it only takes so many cores to saturate a memory bank.
That paper sadly misrepresent Cuckoo Cycle by focusing on an outdated version from the first half of 2014 (and incorrectly describes it as working on directed graphs).