A Self-stabilizing General De Bruijn Graph

  • Michael FeldmannEmail author
  • Christian Scheideler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10616)


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 (\(q = \root d \of {n}\)) 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 \(\mathcal O(\root d \of {n})\), which is asymptotically optimal for a fixed diameter d. The protocol keeps the expected amount of edge redirections per node in \(\mathcal O(\root d \of {n})\), 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.


Distributed systems Topological self-stabilization De bruijn graph 



This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Paderborn UniversityPaderbornGermany

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