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Nice paper!
Algorithm 4, line 14: remove $new$ from $x^{new}_v=x_v+r_v$.
I don't understand the parallelization/scheduling part. May come back to that latter.
I have an implementation of the push method here: https://github.com/maxdan94/push
I will compare the speed.

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full version here : https://link.springer.com/article/10.1007%2Fs00778-020-00602-z
including results with parallelization

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