We consider the problem of constructing a communication infrastructure from scratch, for a collection of identical wireless nodes. Combinatorially, this means a) finding a set of links that form a strongly connected spanning graph on a set of @math points in the plane, and b) scheduling it efficiently in the SINR model of interference. The nodes must converge on a solution in a distributed manner, having no means of communication beyond the sole wireless channel. We give distributed connectivity algorithms that run in time @math , where @math is the ratio between the longest and shortest distances among nodes. Given that algorithm without prior knowledge of the instance are essentially limited to using uniform power, this is close to best possible. Our primary aim, however, is to find efficient structures, measured in the number of slots used in the final schedule of the links. Our main result is algorithms that match the efficiency of centralized solutions. Specifically, the networks can be scheduled in @math slots using (arbitrary) power control, and in @math slots using a simple oblivious power scheme. Additionally, the networks have the desirable properties that the latency of a converge-cast and of any node-to-node communication is optimal @math time.
We study the wireless scheduling problem in the SINR model. More specifically, given a set of @math links, each a sender-receiver pair, we wish to partition (or ) the links into the minimum number of slots, each satisfying interference constraints allowing simultaneous transmission. In the basic problem, all senders transmit with the same uniform power. We give a distributed @math -approximation algorithm for the scheduling problem, matching the best ratio known for centralized algorithms. It holds in arbitrary metric space and for every length-monotone and sublinear power assignment. It is based on an algorithm of Kesselheim and V "ocking, whose analysis we improve by a logarithmic factor. We show that every distributed algorithm uses @math slots to schedule certain instances that require only two slots, which implies that the best possible absolute performance guarantee is logarithmic. In modern wireless networks devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the physical interference model using SINR constraints. In the SINR capacity maximization problem, we are given n pairs of senders and receivers, located in a metric space (usually a so-called fading metric). The algorithm shall select a subset of these pairs and choose a power level for each of them with the objective of maximizing the number of simultaneous communications. This is, the selected pairs have to satisfy the SINR constraints with respect to the chosen powers. We present the first algorithm achieving a constant-factor approximation in fading metrics. The best previous results depend on further network parameters such as the ratio of the maximum and the minimum distance between a sender and its receiver. Expressed only in terms of n, they are (trivial) Ω(n) approximations. Our algorithm still achieves an O(log n) approximation if we only assume to have a general metric space rather than a fading metric. Furthermore, existing approaches work well together with the algorithm allowing it to be used in singlehop and multi-hop scheduling scenarios. Here, we also get polylog n approximations. The capacity of a wireless network is the maximum possible amount of simultaneous communication, taking interference into account. Formally, we treat the following problem. Given is a set of links, each a sender-receiver pair located in a metric space, and an assignment of power to the senders. We seek a maximum subset of links that are feasible in the SINR model: namely, the signal received on each link should be larger than the sum of the interferences from the other links. We give a constant-factor approximation that holds for any length-monotone, sub-linear power assignment and any distance metric. We use this to give essentially tight characterizations of capacity maximization under power control using oblivious power assignments. Specifically, we show that the mean power assignment is optimal for capacity maximization of bi-directional links, and give a tight @math -approximation of scheduling bi-directional links with power control using oblivious power. For uni-directional links we give a nearly optimal @math -approximation to the power control problem using mean power, where @math is the ratio of longest and shortest links. Combined, these results clarify significantly the centralized complexity of wireless communication problems. In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are single-hop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on special-case topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network's topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one time-slot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions. Finally, we show that it is NP-hard to approximate the scheduling problem to within n 1-epsiv factor, for any constant epsiv > 0, in the non-geometric SINR model, in which path-loss is independent of the Euclidean coordinates of the nodes. In this paper we address a common question in wireless communication: How long does it take to satisfy an arbitrary set of wireless communication requests? This problem is known as the wireless scheduling problem. Our main result proves that wireless scheduling is in APX. In addition we present a robustness result, showing that constant parameter and model changes will modify the result only by a constant. We present and analyze simple distributed contention resolution protocols for wireless networks. In our setting, one is given n pairs of senders and receivers located in a metric space. Each sender wants to transmit a signal to its receiver at a prespecified power level, e. g., all senders use the same, uniform power level as it is typically implemented in practice. Our analysis is based on the physical model in which the success of a transmission depends on the Signal-to-Interference-plus-Noise-Ratio (SINR). The objective is to minimize the number of time slots until all signals are successfully transmitted. Our main technical contribution is the introduction of a measure called maximum average affectance enabling us to analyze random contention-resolution algorithms in which each packet is transmitted in each step with a fixed probability depending on the maximum average affectance. We prove that the schedule generated this way is only an O(log2 n) factor longer than the optimal one, provided that the prespecified power levels satisfy natural monontonicity properties. By modifying the algorithm, senders need not to know the maximum average affectance in advance but only static information about the network. In addition, we extend our approach to multi-hop communication achieving the same appoximation factor.