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Publication# Hierarchical Routing Over Dynamic Wireless Networks

Résumé

The topology of a mobile wireless network changes over time. Maintaining routes between all nodes requires the continuous transmission of control information, which consumes precious power and bandwidth resources. Many routing protocols have been developed, trading off control overhead and route quality. In this paper, we ask whether there exist low-overhead schemes that produce low-stretch routes, even in large networks where all the nodes are mobile. We present a scheme that maintains a hierarchical structure within which constant-stretch routes can be efficiently computed between every pair of nodes. The scheme rebuilds each level of the hierarchy periodically, at a rate that decreases exponentially with the level of the hierarchy. We prove that this scheme achieves constant stretch under a mild smoothness condition on the nodal mobility processes. Furthermore, we prove tight bounds for the network-wide control overhead under the additional assumption of the connectivity graph forming a doubling metric space. Specifically, we show that for a connectivity model combining the random geometric graph with obstacles, constant-stretch routes can be maintained with a total overhead of n log2 n bits of control information per time unit.

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Suhas Diggavi, Matthias Grossglauser, Dominique Florian Tschopp

Dynamic networks are those where the topology changes over time and therefore efficient routes need to be maintained by frequent updates. Such updates could be costly in terms of consuming throughput available for data transmission, which is a precious resource in wireless networks. In this paper, we ask the question whether there exist low-overhead schemes for dynamic wireless networks, that could produce routes that are within a small constant factor (stretch) of the optimal route-length. This is studied by using the underlying geometric properties of the connectivity graph in wireless networks. For a class of models for mobile wireless network that fulfill some mild conditions on the connectivity and on mobility over the time of interest, we can design distributed routing algorithm that maintains the routes over a changing topology. This scheme needs only node identities and therefore integrates location service along with routing, therefore accounting for the complete overhead. We analyze the worst-case (conservative) overhead and route-quality (stretch) performance of this algorithm for the aforementioned class of wireless network connectivity and mobility models. In particular for these models, we show that our algorithm allows constant stretch routing with a network wide control traffic overhead of $O(n\log^2 n)$ bits per mobility time step (time-scale of topology change) translating to $O(\log^2 n)$ overhead per node (with high probability for wireless networks with such mobility model). Additionally, we can reduce the maximum overhead per node by using a load-balancing technique at the cost of a slightly higher average overhead. We also demonstrate through numerics that these worst-case bounds are quite conservative in terms of the constants derived theoretically.

2007, , ,

Routing packets is a central function of multi-hop wireless networks. Traditionally, there have been two paradigms for routing, either based on the geographical coordinates of the nodes (geographic routing), or based on the connectivity graph (topology-based routing). The former implicitly assumes that geometry determines connectivity, whereas the latter does not exploit this inherent geometry of wireless networks, and assumes a general graph instead. In this paper, we explore ideas that attempt to bridge these two paradigms. We do so by investigating routing techniques based on metric embeddings of the connectivity graph. If this graph is closely related to the underlying geometry of the nodes, then it is possible to embed the graph in a low-dimensional normed space. This keeps the overhead of the routing protocol low. We specifically explore embeddings of dynamic networks induced by channel fading and mobility. This motivates the novel problem of stable embeddings, where the additional goal is to maintain an embedding over time, such that the evolution of the embedding faithfully captures the evolution of the underlying graph itself. This is crucial to limit the control overhead of the routing protocol, and to ensure that our approach is scalable.

2007, , ,

Wireless routing based on an embedding of the connectivity graph is a very promising technique to overcome shortcomings of geographic routing and topology-based routing. This is of particular interest when either absolute coordinates for geographic routing are unavailable or when they poorly reflect the underlying connectivity in the network. We focus on dynamic networks induced by time-varying fading and mobility. This requires that the embedding is stable over time, whereas the focus of most existing embedding algorithms is on low distortion of single realizations of a graph. We develop a beaconbased distributed embedding algorithm that requires little control overhead, produces low distortion embeddings, and is stable. We also show that a low-dimensional embedding suffices, since at a sufficiently large scale, wireless connectivity graphs are dictated by geometry. The stability of the embedding allows us to combine georouting on the embedding with last encounter routing (LER) for node lookup, further reducing the control overhead. Our routing algorithm avoids dead ends through randomized greedy forwarding. We demonstrate through extensive simulations that our combined embedding and routing scheme outperforms existing algorithms. I. INTRODUCTION

2007