In the paper 'A Simple and Strongly-Local Flow-Based Method for Cut Improvement', the authors mentioned that the strongly-local spectral methods have shown much stronger results, where the algorithm doesn’t even access most of the nodes of the graph and thus the running time is dependent on the size of the seed set or output set, rather than the entire graph. These strongly-local spectral algorithms are very fast in both theory and practice, which is supported by another paper that you've read, please provide the full name of that paper.