New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. This naturally engenders new route-discovery problems under changing conditions over these networks. Unfortunately, the temporal variations in the network topology are hard to be effectively captured in a classical graph model. In this paper, we use and extend a recently proposed graph theoretic model, which helps capture the evolving characteristic of such networks, in order to propose and formally analyze least cost journey (the analog of paths in usual graphs) in a class of dynamic networks, where the changes in the topology can be predicted in advance. Cost measures investigated here are hop count (shortest journeys), arrival date (foremost journeys), and time span (fastest journeys).

Abstract. We consider the problem of data propagation in wireless sensor networks and revisit the family of mixed strategy routing schemes. We show that maximizing the lifespan, balancing the energy among individual sensors and maximizing the message flow in the network are equivalent. We propose a distributed and adaptive data propagation algorithm for balancing the energy among sensors in the network. The mixed routing algorithm we propose allows each sensor node to either send a message to one of its immediate neighbors, or to send it directly to the base station, the decision being based on a potential function depending on its remaining energy. By considering a simple model of the network and using a linear programming description of the message flow, we prove the strong result that an energy-balanced mixed strategy beats every other possible routing strategy in terms of lifespan maximization. Moreover, we provide sufficient conditions for ensuring the dynamic stability of the algorithm. The algorithm is inspired by the gradient-based routing scheme but by allowing to send messages directly to the base station we improve considerably the lifespan of the network. As a matter of fact, we show experimentally that our algorithm is close to optimal and that it even beats the best centralized multi-hop routing strategy.

Abstract.A wide range of applications in wireless sensor networks rely on the location information of the sensing nodes. However, traditional localization techniques are dependent on hardware that is sometimes unavailable (e.g. GPS), or on sophisticated virtual localization calculus which have a costly overhead.Instead of actually localizing nodes in the physical two-dimensional Euclidean space, we use directly the raw distance to a set of anchors to produce multi-dimensional coordinates. We prove that the image of the physical two-dimensional Euclidean space is a two-dimensional surface, and we show that it is possible to adapt geographic routing strategies on this surface, simply, efficiently and successfully.

Abstract-In this paper, we propose an efficient planarization algorithm and a routing algorithm dedicated to Unit Disk Graphs whose nodes are localized using the Virtual Raw Anchor Coordinate system (VRAC). Our first algorithm computes a planar 2-spanner under light constraints on the edge lengths and induces a total exchange of at most 6n node identifiers. Its total computational complexity is O(n∆), with ∆ the maximum degree of the communication graph. The second algorithm that we present is a simple and efficient algorithm to route messages in this planar graph that requires routing tables with only three entries. We support these theoretical results by simulations showing the robustness of our algorithms when the coordinates are inaccurate.

Abstract. This paper studies the data gathering problem in wireless networks, where data generated at the nodes has to be collected at a single sink. We investigate the relationship between routing optimality and fair resource management. In particular, we prove that for energy balanced data propagation, Pareto optimal routing and flow maximization are equivalent, and also prove that flow maximization is equivalent to maximizing the network lifetime. We algebraically characterize the network structures in which energy balanced data flows are maximal. Moreover, we algebraically characterize communication links which are not used by an optimal flow. This leads to the characterization of minimal network structures supporting the maximal flows. We note that energy balance, although implying global optimality, is a local property that can be computed efficiently and in a distributed manner. We suggest online distributed algorithms for energy balance in different optimal network structures and numerically show their stability in particular setting. We remark that although the results obtained in this paper have a direct consequence in energy saving for wireless networks they do not limit themselves to this type of networks neither to energy as a resource. As a matter of fact, the results are much more general and can be used for any type of network and different types of resources. 3