Deterministic routing on circular arrays

The authors analyze the routing of k-permutations on circular processor arrays connected by bidirectional links. In contrast to linear processor arrays, it is hard to prove lower bounds for the routing time or to construct efficient algorithms for routing k-permutations on circular arrays (except for the case k =1). The authors prove nontrivial lower bounds for routing with global knowledge and for routing with local knowledge. They present deterministic algorithms that use local information only. The best of these algorithms requires only k×n/4+emsn routing steps for all k⩾4. This almost matches the k×n/4 lower bound. Special attention is given to the cases k=2 and 3