Routing on the PADAM: Degrees of Optimality

Routing problems are studied for the Parallel Alternating-Direction Access Machine. The goal is to investigate what level of optimality can be achieved depending on loads of packets per memory unit. In the case of typical moderate loads, our algorithms are optimal to within a small multiplicative constant; a deterministic and a randomized algorithm are developed, both faster than the best previously known routing algorithm. Moreover, for sufficiently large loads, an algorithm which misses optimality by only an additive lower-order term is designed. We consider also off-line routing problems, and multidimensional extension of the model