Scheduling in wireless ad hoc networks: algorithms with performance guarantees

The traditional disk graph based approach to wireless ad hoc network scheduling relies on an overly simplified physical layer model. Consequently, it cannot provide any guarantee on the accuracy of the solution. On the other hand, the recent optimization theoretic approach uses more detailed physical layer models for accuracy. However, in this case, the scheduling problem becomes non-convex (or combinatorial), and hence, its solution is computationally intractable. In this context, we attempt to develop computationally efficient scheduling algorithms with performance guarantees. This goal is achieved by utilizing different types of structures in the problem that are relevant to reducing the complexity of scheduling. First, we begin by considering some restrictive conditions such as a low signal to noise ratio or few transmitters, which introduce special algebraic structures. These algebraic structures are successfully utilized to solve the scheduling problem optimally, with complexity lower than that indicated by the pure optimization approach. Next, we design algorithms applicable to more general and larger ad hoc networks. The key to the design of such algorithms is the special geometric structure, resulting from the physical properties of the wireless medium. We apply appropriate algorithmic techniques so that the geometric structure can be exploited to trade off the accuracy of the algorithm and its complexity. Consequently, approximation algorithms with complexity polynomial in the number of links n are obtained. Finally, we design a very low complexity (O(n2 log n)) algorithm with a probabilistic guarantee, utilizing the stochastic symmetry in a random network with independent and identically distributed links. A probabilistic analysis shows that, with high probability, the number of channels required by the algorithm is of the same order as the minimum required number of channels. In addition to the mathematical analysis proving these theoretical results, some simulations are performed for various ad hoc network scenarios. The obtained results demonstrate the practical utility of the presented algorithms as a wireless ad hoc network design tool.