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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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