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

On Compact Routing for the Internet

While there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer routing tables of sizes that scale logarithmically with the network size, we demonstrate in this paper that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic routing table size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802

Names, addresses and identities in ambient networks

Ambient Networks interconnect independent realms that may use different local network technologies and may belong to different administrative or legal entities. At the core of these advanced internetworking concepts is a flexible naming architecture based on dynamic indirections between names, addresses and identities. This paper gives an overview of the connectivity abstractions of Ambient Networks and then describes its naming architecture in detail, comparing and contrasting them to other related next-generation network architectures

Fast Routing Table Construction Using Small Messages

We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of the graph when all edges are considered to have unit weight. Given 0 < eps <= 1/2, our algorithm runs in weak-O(n^(1/2 + eps) + HD) communication rounds using messages of O(log n) bits and guarantees a stretch of O(eps^(-1) log eps^(-1)) with high probability. This is the first distributed algorithm approximating weighted shortest paths that uses small messages and runs in weak-o(n) time (in graphs where HD in weak-o(n)). The time complexity nearly matches the lower bounds of weak-Omega(sqrt(n) + HD) in the small-messages model that hold for stateless routing (where routing decisions do not depend on the traversed path) as well as approximation of the weigthed diameter. Our scheme replaces the original identifiers of the nodes by labels of size O(log eps^(-1) log n). We show that no algorithm that keeps the original identifiers and runs for weak-o(n) rounds can achieve a polylogarithmic approximation ratio. Variations of our techniques yield a number of fast distributed approximation algorithms solving related problems using small messages. Specifically, we present algorithms that run in weak-O(n^(1/2 + eps) + HD) rounds for a given 0 < eps <= 1/2, and solve, with high probability, the following problems: - O(eps^(-1))-approximation for the Generalized Steiner Forest (the running time in this case has an additive weak-O(t^(1 + 2eps)) term, where t is the number of terminals); - O(eps^(-2))-approximation of weighted distances, using node labels of size O(eps^(-1) log n) and weak-O(n^(eps)) bits of memory per node; - O(eps^(-1))-approximation of the weighted diameter; - O(eps^(-3))-approximate shortest paths using the labels 1,...,n.Comment: 40 pages, 2 figures, extended abstract submitted to STOC'1

Compact Routing on Internet-Like Graphs

The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme on random graphs with power-law node degree distributions, $P_k \sim k^{-\gamma}$. We find that the average stretch is very low and virtually independent of $\gamma$. In particular, for the Internet interdomain graph, $\gamma \sim 2.1$, the average stretch is around 1.1, with up to 70% of paths being shortest. As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for $10^4$-node networks. Furthermore, we find that both the average shortest path length (i.e. distance) $\bar{d}$ and width of the distance distribution $\sigma$ observed in the real Internet inter-AS graph have values that are very close to the minimums of the average stretch in the $\bar{d}$- and $\sigma$-directions. This leads us to the discovery of a unique critical quasi-stationary point of the average TZ stretch as a function of $\bar{d}$ and $\sigma$. The Internet distance distribution is located in a close neighborhood of this point. This observation suggests the analytical structure of the average stretch function may be an indirect indicator of some hidden optimization criteria influencing the Internet's interdomain topology evolution.Comment: 29 pages, 16 figure

Confidentiality-Preserving Publish/Subscribe: A Survey

Publish/subscribe (pub/sub) is an attractive communication paradigm for large-scale distributed applications running across multiple administrative domains. Pub/sub allows event-based information dissemination based on constraints on the nature of the data rather than on pre-established communication channels. It is a natural fit for deployment in untrusted environments such as public clouds linking applications across multiple sites. However, pub/sub in untrusted environments lead to major confidentiality concerns stemming from the content-centric nature of the communications. This survey classifies and analyzes different approaches to confidentiality preservation for pub/sub, from applications of trust and access control models to novel encryption techniques. It provides an overview of the current challenges posed by confidentiality concerns and points to future research directions in this promising field

Local Approximation Schemes for Ad Hoc and Sensor Networks

We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs