Listing acyclic orientations of graphs with single and multiple sources

We study enumeration problems for the acyclic orientations of an undirected graph with n nodes and m edges, where each edge must be assigned a direction so that the resulting directed graph is acyclic. When the acyclic orientations have single or multiple sources specified as input along with the graph, our algorithm is the first one to provide guaranteed bounds, giving new bounds with a delay of O(m・n) time per solution and O(n2) working space. When no sources are specified, our algorithm improves over previous work by reducing the delay to O(m), and is the first one with linear delay. © Springer International Publishing Switzerland 2016.