On Hypercube Routing and Fault Tolerance with Bit Constraint

Due to their simplicity, hyper cubes are very popular as interconnection networks of parallel systems. While several routing algorithms have been described for this network topology in the literature, we consider in this paper hypercube routing with an additional restriction: bit constraint. Simply speaking, routing will be conducted amongst a particular subset of nodes, all of which must satisfy a condition regarding their bit weights (a.k.a. Hamming weights). Such kind of routing restriction has several applications including simplification of disjoint paths routing and hypercube embedded network routing. In this paper, we describe two hypercube routing algorithms satisfying such restriction, the first one for shortest-path routing and the second one for fault-tolerant point-to-point routing. Correctness and complexities of the proposed algorithms are formally proved. The shortest-path routing algorithm described is shown to be time-optimal. Lastly, an empirical evaluation of the proposed algorithm is conducted in order to inspect its practical behaviour.