Permutation routing in double-loop networks: design and empirical evaluation

A double-loop network is an undirected graph whose nodes are integers 0, 1,..., n-1 and each node a is adjacent to four nodes u +/- h(1) (mod > n), u +/- h(2) (mod > n), where 0 < h(1) < h(2) < n/2. There are initially n packets, one at each of the n nodes. The packet at node a is destined to node pi(u), where the mapping u-->pi(u) is a permutation. The aim is to minimize the number of routing steps to route all the packets to their destinations. If P is the tight lower bound for this number, then the best known permutation routing algorithm takes, on average, 1.98l routing steps (and 2l routing steps in the worst-case). Because the worst-case complexity cannot be improved, we design four new static permutation routing algorithms with gradually improved average-case performances, which are 1.37l, 1.35l, 1.18l, and 1.12l. Thus, the best of these algorithms exceeds the optimal routing by at most 12% on average. To support our algorithm design we develop a program which simulates permutation routing in a network according to the given topology, routing model as well as communication pattern and measure several quality criteria. We have tested our algorithms on a large number of double-loop networks and permutations (randomly generated and standard). (C) 2003 Elsevier Science B.V. All rights reserved.