Deterministic Routing on Circular Arrays

We 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 eecient algorithms for routing k-permutations on circular arrays (except for the case k = 1). We will prove non-trivial lower bounds for routing with global knowledge and for routing with local knowledge. Then we present oblivious deterministic algorithms that use local information only. The best of these algorithms requires only k n=4 + p n 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.