We generalize three existing graph algorithms to compute the provenance of regular path queries over graph databases, in the framework of provenance semirings – algebraic structures that can capture different forms of provenance. Each algorithm yields a different trade-off between time complexity and generality, as each requires different properties over the semiring. Together, these algorithms cover a large class of semirings used for provenance (top-k, security, etc.). Experimental results suggest these approaches are complementary and practical for various kinds of provenance indications, even on a relatively large transport network.