Dominique Tschopp

Robust Geo-Routing on Embeddings of Dynamic Wireless Networks

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 beacon-based 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 geo-routing 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.

Facebrowsing: Search and navigation through comparisons

This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object in a database which is only accessible through a comparison oracle. The comparison oracle, given two reference objects and a query object, returns the reference object closest to the query object. The oracle attempts to model the behavior of human users, capable of making statements about similarity, but not of assigning meaningful numerical values to distances between objects. We develop nearest-neighbor search algorithms and analyze its performance for such an oracles. Using such a comparison oracle, the best we can hope for is to obtain, for every object in the database, a ranking of the other objects according to their distance to it. The difficulty of searching using such an oracle depends on the non-homogeneities of the underlying space. We introduce the new idea of a ranksensitive hash (RSH) function which gives same hash value for “similar” objects based on the rank-value of the objects obtained from the similarity oracle. As one application of RSH, we demonstrate that, we can retrieve one of the (1 + ∊)τ-nearest neighbor of a query point in time-complexity depending on an underlying property (termed rank-distortion) of the search space. We use this idea to implement a navigation system for an image database of human faces. In particular, we design a database for images that is organized adaptively based on both baseline comparisons using eigenfaces and refined using selected human input. We present a preliminary implementation of this system which seeks to minimize the number of questions asked to a (human) oracle.

Robust Routing for Dynamic Wireless Networks Based on Stable Embeddings

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.

Hierarchical routing over dynamic wireless networks

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 nlog2n bits of control information per time unit.

Routing in Mobile Wireless Networks

A major challenge in the design of wireless ad hoc networks is the need for distributed routing algorithms that consume a minimal amount of network resources. This is particularly important in dynamic networks, where the topology can change over time, and therefore routing tables must be updated frequently. Such updates incur control traffic, which consumes bandwidth and power.