We present a new method for finding k shortest paths between any two vertices in the Cayley graph \(\text {Cay}(G, S)\) of a finite group G with its generating set S closed under inverses. By using a reduced convergent rewriting system R for G, we first find the lexicographically minimal shortest path between two vertices in \(\text {Cay}(G, S)\) . Then, by symmetrizing the length-preserving rules of R, we provide a polynomial time algorithm (in the size of certain rewrite rules, the lexicographically minimal shortest path, and k) for finding k shortest paths between two vertices in \(\text {Cay}(G, S)\) . Our implementation of finding k shortest paths between two vertices in \(\text {Cay}(G, S)\) is also discussed.
