A column generation method for spatial TDMA scheduling in ad hoc networks

An ad hoc network can be set up by a number of units without the need of any permanent infrastructure. Two units establish a communication link, if the channel quality is sufficiently high. As not all pairs of units can establish direct links, the traffic between two units may have to be relayed through other units. This is known as the multi-hop functionality. In military command and control systems, ad hoc networks are also referred to as multi-hop radio networks. Spatial TDMA (STDMA) is a scheme for access control in ad hoc networks. STDMA improves TDMA by allowing simultaneous transmission of multiple units. In this paper, we study the problem of STDMA scheduling, where the objective is to find minimum-length schedules. Previous work for this problem has focused on heuristics, whose performance is difficult to analyze when optimal solutions are not known. We develop novel mathematical programming formulations for this problem, and present a column generation solution method. Our numerical experiments show that the method generates a very tight bound to the optimal schedule length, and thereby enables optimal or near-optimal solutions. The column generation method can be used to provide benchmarks when evaluating other scheduling algorithms. In particular, we use the bound obtained in the column generation method to evaluate a simple greedy algorithm that is suitable for distributed implementations.