Resource optimization of spatial TDMA in ad hoc radio networks: a column generation approach

Wireless communications using ad hoc networks are receiving an increasing interest. The most attractive feature of ad hoc networks is the flexibility. The network is set up by a number of units in an ad hoc manner, without the need of any fixed infrastructure. Communication links are established between two units if the signal strength is sufficiently high. As not all pairs of nodes can establish direct links, the traffic between two units may have to be relayed through other units. This is known as the multihop functionality. Design of ad hoc networks is a challenging task. In this paper we study the problem of resource allocation with spatial TDMA (STDMA) as the access control scheme. Previous work for this problem has mainly focused on heuristics, whose performance is difficult to analyze when optimal solutions are not known. We develop, for both node-oriented and link-oriented allocation strategies, mathematical programming formulations for resource optimization. We further present a column generation approach, which, in our numerical experiments, constantly yields optimal or near-optimal solutions. Our results provide important benchmarks when evaluating heuristic on-line algorithms for resource optimization using STDMA.