For a vertex u ∈ Vi and every other Vj, an edge has to connect u to some v ∈ Vj in any alignment. When calculating Fu, we can constrain its value by considering three-way alignments and requiring that the vertices in the best star(u) chosen as neighbors of u in graph parts other than Vj are also good matches to v. Performing this computation for every pair of u, Vj and considering every edge incident on u would be too costly. Therefore, we only consider such three-way alignments for every vertex u ∈ Vi and the next part Vi+1 of the graph (with the last and first parts paired). Essentially, this procedure shifts the emphasis onto edges, allowing better alignments and bounds, and yet eliminates vertices by considering the best edge incident on it.