Structure and algorithms in the SINR wireless model
ACM SIGACT News
Connectivity problem in wireless networks
DISC'10 Proceedings of the 24th international conference on Distributed computing
Efficiency of Wireless Networks: Approximation Algorithms for the Physical Interference Model
Foundations and Trends® in Networking
Minimum latency data aggregation in the physical interference model
Proceedings of the 14th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems
A note on uniform power connectivity in the physical signal to interference plus noise (SINR) model
Theoretical Computer Science
Minimum latency data aggregation in the physical interference model
Computer Communications
Broadcasting in logarithmic time for ad hoc network nodes on a line using mimo
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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Modeling communications in wireless networks is a challenging task, since it requires a simple mathematical object on which efficient algorithms can be designed but which must also reflect the complex physical constraints inherent in wireless networks, such as interferences, the lack of global knowledge, and purely local computations. As a tractable mathematical object, the unit disk graph (UDG) is a popular model that has enabled the development of efficient algorithms for crucial networking problems. In a ρ-UDG, two nodes are connected if and only if their distance is at most ρ, for some ρ ≪ 0. However, such a connectivity requirement is basically not compatible with the reality of wireless networks due to the environment of the nodes as well as the constraints of radio transmission. For this purpose, the signal interference plus noise ratio model (SINR) is the more commonly used model. The SINR model focuses on radio interferences created over the network depending on the distance to transmitters. Nevertheless, due to its complexity, this latter model has been the subject of very few theoretical investigations and lacks of good algorithmic features. In this paper, we demonstrate how careful scheduling of the nodes enables the two models to be combined to give the benefits of both the algorithmic features of the UDG and the physical validity of the SINR. Precisely, we show that it is possible to emulate a 1/√n ln n-UDG that satisfies the constraints of the SINR over any set of n wireless nodes distributed uniformly in a unit square, with only a O(ln3 n) time and power stretch factor. The main strength of our contribution lies in the fact that the scheduling is set in a fully distributed way and considers non-uniform power ranges, and it can therefore fit the sensor network setting. Moreover, our scheduling is optimal up to a polylogarithmic factor in terms of throughput capacity according to the lower bound of Gupta and Kumar.