Beyond Geometry : Towards Fully Realistic Wireless Models

Signal-strength models of wireless communications capture the gradual fading of signals and the additivity of interference. As such, they are closer to reality than other models. However, nearly all theoretic work in the SINR model depends on the assumption of smooth geometric decay, one that is true in free space but is far off in actual environments. The challenge is to model realistic environments, including walls, obstacles, reflections and anisotropic antennas, without making the models algorithmically impractical or analytically intractable. We present a simple solution that allows the modeling of arbitrary static situations by moving from geometry to arbitrary decay spaces. The complexity of a setting is captured by a metricity parameter Z that indicates how far the decay space is from satisfying the triangular inequality. All results that hold in the SINR model in general metrics carry over to decay spaces, with the resulting time complexity and approximation depending on Z in the same way that the original results depends on the path loss term alpha. For distributed algorithms, that to date have appeared to necessarily depend on the planarity, we indicate how they can be adapted to arbitrary decay spaces. Finally, we explore the dependence on Z in the approximability of core problems. In particular, we observe that the capacity maximization problem has exponential upper and lower bounds in terms of Z in general decay spaces. In Euclidean metrics and related growth-bounded decay spaces, the performance depends on the exact metricity definition, with a polynomial upper bound in terms of Z, but an exponential lower bound in terms of a variant parameter phi. On the plane, the upper bound result actually yields the first approximation of a capacity-type SINR problem that is subexponential in alpha

Dynamic Packet Scheduling in Wireless Networks

We consider protocols that serve communication requests arising over time in a wireless network that is subject to interference. Unlike previous approaches, we take the geometry of the network and power control into account, both allowing to increase the network's performance significantly. We introduce a stochastic and an adversarial model to bound the packet injection. Although taken as the primary motivation, this approach is not only suitable for models based on the signal-to-interference-plus-noise ratio (SINR). It also covers virtually all other common interference models, for example the multiple-access channel, the radio-network model, the protocol model, and distance-2 matching. Packet-routing networks allowing each edge or each node to transmit or receive one packet at a time can be modeled as well. Starting from algorithms for the respective scheduling problem with static transmission requests, we build distributed stable protocols. This is more involved than in previous, similar approaches because the algorithms we consider do not necessarily scale linearly when scaling the input instance. We can guarantee a throughput that is as large as the one of the original static algorithm. In particular, for SINR models the competitive ratios of the protocol in comparison to optimal ones in the respective model are between constant and O(log^2 m) for a network of size m.Comment: 23 page