Off-line permutation scheduling on circuit-switched fixed routing networks

The problem of offline permutation scheduling on linear arrays, rings, hypercubes, and two-dimensional arrays, assuming the CSFR (circuit-switched fixed routing) model, is examined. Optimal permutation scheduling involves finding a minimum number of subsets of nonconflicting source-destination paths. Every subset of paths can be established to run in one pass. Optimal permutation scheduling on linear arrays is shown to be linear and on rings NP-complete. On hypercubes, the problem is NP-complete. However, the author discusses an O( N log N) algorithm that routes any permutation in two passes if the model is relaxed to allow for two routing rules, the e -cube rule and the e^-1-cube rule. This complexity is reduced to O(N) hypercube-parallel time. An O(N log² N) bipartite-matching-based algorithm designed to schedule any permutation on p×q meshes/tori in q passes is considered