I have a reasonable understanding of the technique to detect similar documents consisting in first computing their minhash signatures (from their shingles, or n-grams), and then use an LSH-based algorithm to cluster them efficiently (i.e. avoid the quadratic complexity which would entail a naive pairwise exhaustive search).
What I'm trying to do is to bridge three different algorithms, which I think are all related to this minhash + LSH framework, but in non-obvious ways:
The algorithm sketched in Section 3.4.3 of Chapter 3 of the book Mining of Massive Datasets (Rajaraman and Ullman), which seems to be the canonical description of minhashing
Ryan Moulton's Simple Simhashing article
Charikar's so-called SimHash algorihm, described in this article
I find this confusing because what I assume is that although  uses the term "simhashing", it's actually doing minhashing in a way similar to , but with the crucial difference that a cluster can only be represented by a single signature (even tough multiple hash functions might be involved), while two documents have more chances of being similar with , because the signatures can collide in multiple "bands".  seems like a different beast altogether, in that the signatures are compared in terms of their Hamming distance, and the LSH technique implies multiple sorting of the signatures, instead of banding them. I also saw (somewhere else) that this last technique can incorporate a notion of weighting, which can be used to put more emphasis on certain document parts, and which seems to lack in  and .
So at last, my two questions:
Is there a (satisfying) way in which to bridge those three algorithms?
Is there a way to import this notion of weighting from  into ?