In the following it is assumed that the graph partition is stored on processing elements (PE) which are labeled formula_4. Each PE initializes a set of local vertices formula_5 with indegree 0, where the upper index represents the current iteration. Since all vertices in the local sets formula_6 have indegree 0, i.e. they are not adjacent, they can be given in an arbitrary order for a valid topological sorting. To assign a global index to each vertex, a prefix sum is calculated over the sizes of formula_6. So each step, there are formula_8 vertices added to the topological sorting.