Global optimisation via s-t graph cuts is widely used in computer vision and graphics. To obtain high-resolution output, graph cut methods must construct massive N-D grid-graphs containing billions of vertices. We show that when these graphs do not fit into physical memory, current max-flow/min-cut algorithms-the workhorse of graph cut methods-are totally impractical. Others have resorted to banded or hierarchical approximation methods that get trapped in local minima, which loses the main benefit of global optimisation. We enhance the push-relabel algorithm for maximum flow [14] with two practical contributions. First, true global minima can now be computed on immense grid-like graphs too large for physical memory. These graphs are ubiquitous in computer vision, medical imaging and graphics. Second, for commodity multi-core platforms our algorithm attains near-linear speedup with respect to number of processors. To achieve these goals, we generalised the standard relabeling operations associated with push-relabel.