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Open Access Publications from the University of California

Lowest common ancestor interconnection networks


Lowest Common Ancestor (LCA) networks are built using switches capable of connecting u + d inputs/outputs in a permutation pattern. For n source nodes and I stages of switches, n/d switches are used in stage l - n/d - u/d in stage l - 2, and in general , n-u^l-i-l/d^l-i switches in stage i. The resulting hierarchical structure possesses interesting connectivity and permutational properties. A full characterization of LCA networks is presented together with a permutation routing algorithm for a family of LCA networks. The algorithm uses the network itself to collect and disseminate information about the permutation. A schedule of O(dp log_d/u n) passes is obtained with a switch set-up cost factor of O(log_d/u n) (p is the minimum number of passes that an algorithm with global knowledge schedules).

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