Year: 2024
Type: article
Abstract: We present a new method for finding k shortest paths between any two vertices in the Cayley graph $$\text {Cay}(G, S)$$ 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 $$\text {Cay}(G, S)$$ 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 $$\text {Cay}(G, S)$$ Cay ( G , S ) . Our implementation of finding k shortest paths between two vertices in $$\text {Cay}(G, S)$$ Cay ( G , S ) is also discussed.
Source: Graphs and Combinatorics
Author: Dohan Kim
Institution: Universität Innsbruck
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4404130784