Disclosed are improved methods and mechanisms for congestion and maximum flow analysis for routing an integrated circuit design. In one approach, maximum flow analysis is performed by tessellating a portion of a layout to form space tiles, which are used to interpret a flow graph. The flow graph comprises a set of vertices and edges. The capacity of edges in the flow graph is used to identify the maximum flow for that portion of the layout. In another approach, an edge walk is performed against a set of space tiles, in which a nearest neighbor determination is determined for each edge to perform maximum flow analysis.