Finding k Shortest Paths in Cayley Graphs of Finite Groups

We present a new method for finding k shortest paths between any two vertices in the Cayley graph 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 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 Cay ( G , S ) . Our implementation of finding k shortest paths between two vertices in Cay ( G , S ) is also discussed.