Comment by srean

At the core both derive their optimization from the distributive property. If the expression graph has symmetry, you get more optimization out of it.

https://www.cs.ubc.ca/~murphyk/Teaching/Papers/GDL.pdf

Check out the first paragraph

    THE humble distributive
    law, in its simplest form
    states that...this leads
    to a large family of fast
    algorithms, including 
    Viterbi’s algorithm and 
    the fast Fourier
    transform (FFT).

Two extremely influential papers appeared back to back in transactions information theory. This is one of them.

The other is

https://vision.unipv.it/IA2/Factor graphs and the sum-product algorithm.pdf

Both are absolute gems of papers. The editor made sure that both appear in the same volume.