On the Communication Complexity of Distributed Name-Independent Routing Schemes

Cyril Gavoille (1, 2) , Christian Glacet (1, 3) , Nicolas Hanusse (1) , David Ilcinkas (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IUF - Institut universitaire de France
3 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms

We present a distributed asynchronous algorithm that, for every undirected weighted $n$-node graph $G$, constructs name-independent routing tables for $G$. The size of each table is $\tO(\sqrt{n}\,)$, whereas the length of any route is stretched by a factor of at most~$7$ w.r.t. the shortest path. At any step, the memory space of each node is $\tO(\sqrt{n}\,)$. The algorithm terminates in time $O(D)$, where $D$ is the hop-diameter of $G$. In synchronous scenarios and with uniform weights, it consumes $\tO(m\sqrt{n} + n^{3/2}\min\set{D,\sqrt{n}\,})$ messages, where $m$ is the number of edges of $G$. In the realistic case of sparse networks of poly-logarithmic diameter, the communication complexity of our scheme, that is $\tO(n^{3/2})$, improves by a factor of $\sqrt{n}$ the communication complexity of \emph{any} shortest-path routing scheme on the same family of networks. This factor is provable thanks to a new lower bound of independent interest.

Mots clés: distributed routing algorithm; name-independent; compact routing; bounded stretch

Domaines: Algorithme et structure de données [cs.DS]; Calcul parallèle, distribué et partagé [cs.DC]

Cyril Gavoille, Christian Glacet, Nicolas Hanusse, David Ilcinkas. On the Communication Complexity of Distributed Name-Independent Routing Schemes. DISC 2013, Oct 2013, Jérusalem, Israel. pp.418-432. ⟨hal-00851217⟩