On the Communication Complexity of Distributed Name-Independent Routing Schemes

International audienceWe 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

Disconnected components detection and rooted shortest-path tree maintenance in networks

International audienceMany articles deal with the problem of maintaining a rooted shortest-path tree. However, after some edge deletions, some nodes can be disconnected from the connected component $V_r$ of some distinguished node $r$. In this case, an additional objective is to ensure the detection of the disconnection by the nodes that no longer belong to $V_r$. We present a detailed analysis of a silent self-stabilizing algorithm. We prove that it solves this more demanding task in anonymous weighted networks with the following additional strong properties: it runs without any knowledge on the network and under the \emph{unfair} daemon, that is without any assumption on the asynchronous model. Moreover, it terminates in less than $2n+D$ rounds for a network of $n$ nodes and hop-diameter $D$

On the Communication Complexity of Distributed Name-Independent Routing Schemes

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 Õ(√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 Õ(√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 Õ(m √ n + n 3/2 min {D, √ 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 Õ(n3/2), improves by a factor of √ n the communication complexity of any shortest-path routing scheme on the same family of networks. This factor is provable thanks to a new lower bound of independent interest