Abstract
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.
Published Version
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