Finding the minimum ratio cut or normalised cut is computationally prohibitive approximation is often used

One common approximation algorithm used to find the minimum ratio cut or normalized cut is the spectral clustering algorithm. This algorithm involves computing the eigenvectors of the graph Laplacian matrix and using them to cluster the data points into two or more groups. This approach has been shown to have good performance in practice and is widely used in various applications such as image segmentation, community detection, and data clustering. Other approximation algorithms include recursive bisection, Kernighan-Lin algorithm, and Fiduccia-Mattheyses algorithm. These algorithms offer a trade-off between the quality of the cut and the computational complexity, making them suitable for large-scale problems