A Weighted Graph Partitioning Problem with Side Constraints - HUM, Sin Hoon (Institutional Knowledge at Singapore Management University, 1992)
This paper considers a weighted-graph partitioning problem with side capacity constraints and a special underlying structure: certain nodes are already preassigned to partitions of the graph. We exploit the special underlying structure to make the graph partitioning problem into a maximum flow network problem with side constraints. We propose an algorithm for solving our problem based on the generic version of the preflow-push algorithm for the maximum flow network problem. Also, our algorithm incorporates heuristic approaches to generate close to optimal solutions which are also feasible with regards to the side capacity constraints.