An efficient method for finding a minimal feedback arc set in directed graphs

Finding a minimum cardinality set of arcs that breaks all cycles in a directed graph is important in the study of large-scale systems with feedback. This problem is viewed as finding an ordering for the vertices in a graph such that the set of arcs from higher to lower numbered vertices becomes minimum. After partitioning the graph into strongly and bi-connected components, depth-first search traversing is performed on each component. Reordering is done so that only backward arcs become negative arcs. An efficient cutting technique to reduce the negative arcs further is then described. Experimental results for a number of directed graphs are given