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How does it work? Please explain in enough detail in English or pseudocode so that I can implement in any language.

It is mentioned and briefly described in this paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.4.3643&rep=rep1&type=pdf

but there isn't enough detail there to implement myself. (the weights in Fig2b seem wrong? and it's not clear how they decided where to make the cuts in Fig 2c.)

I also looked up the original source paper (http://www-2.cs.cmu.edu/~glmiller/Publications/Papers/ReMiMo93.pdf) but couldn't figure it out from there either.

Are there better algorithms out there that fill the same need? Specifically, anything that can guarantee partitioned trees that are "almost the same size" (but more so)? The paper suggests m-bridge guarantees no partitioned tree to be bigger than 4n/p, which is not much of a guarantee if you only have 4 processors!