Hot-potato algorithms for permutation routing

We develop a methodology for the design of hot-potato algorithms for routing permutations. The basic idea is to convert existing store-and-forward routing algorithms to hot-potato algorithms. Using it, we obtain the following complexity bounds for permutation routing: n×n Mesh: 7n+o(n) steps; 2ⁿ hypercube: O(n²) steps; n×n Torus: 4n+o(n) steps. The algorithm for the two-dimensional grid is the first to be both deterministic and asymptotically optimal. The algorithm for the 2ⁿ-nodes Boolean cube is the first deterministic algorithm that achieves a complexity of o(2ⁿ) steps