A Self-stabilizing General De Bruijn Graph

Searching for other participants is one of the most important operations in a distributed system. We are interested in topologies in which it is possible to route a packet in a fixed number of hops until it arrives at its destination. Given a constant d, this paper introduces a new self-stabilizing protocol for the q-ary d-dimensional de Bruijn graph (q = d root n) that is able to route any search request in at most d hops w.h.p., while significantly lowering the node degree compared to the clique: We require nodes to have a degree of O(d root n), which is asymptotically optimal for a fixed diameter d. The protocol keeps the expected amount of edge redirections per node in O(d root n), when the number of nodes in the system increases by factor 2(d). The number of messages that are periodically sent out by nodes is constant.