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/spl times Mesh: 7n+o(n) steps; 2/sup n/ hypercube: O(n/sup 2/) steps; n/spl times 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 2/sup n/-nodes Boolean cube is the first deterministic algorithm that achieves a complexity of o(2/sup n/) steps.
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机译：我们开发了一种设计用于路由排列的热土豆算法的方法。基本思想是将现有的存储转发路由算法转换为热土豆算法。使用它，我们为置换路由获得了以下复杂度界限：n / spl次/ n网格：7n + o（n）个步骤； 2 / sup n /超立方体：O（n / sup 2 /）个步骤； n / spl次/ n Torus：4n + o（n）步。二维网格算法首先是确定性和渐近最优的。 2 / sup n /个节点布尔立方体的算法是第一种确定性算法，实现了o（2 / sup n /）个步骤的复杂性。
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