Finding Balance-Fair Short Paths in Graphs

The computation of short paths in graphs with edge lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. We contribute to a broader view on path finding by injecting a natural fairness aspect. Our fairness notion relates to vertex-colored graphs. Herein, we seek to find short paths in which all colors should appear with roughly the same frequency. Among other results, we prove the introduced problems to be computationally intractable (NP-hard and parameterized hard with respect to the number of colors), while also presenting an encouraging algorithmic result ("fixed-parameter tractability") related to the length of the sought solution path.