A generalized topological sorting problem

Abstract

Motivated by an application in the design of VLSI layouts, we consider a generalization of the usual topological sorting problem on directed, acyclic graphs. The difference is that an instance of the generalized problem may require some nodes in the graph to occupy fixed positions in the topological order. We also allow several nodes to share the same position in the topological order.

We describe an algorithm to decide whether a generalized topological sorting problem has a solution and if so, to find a solution and to test whether the solution is unique. The algorithm runs in O(e + n log log n) time on a directed, acyclic graph with n nodes and e edges and in linear time on the graphs arising in our application.