Toward Tractable Computation of the Capacity of Multi-Hop Wireless Networks

By posing the problem of bandwidth allocation as a constrained maximization problem, it is possible to study various features of optimal bandwidth allocation, and hence the capacity of the network. However, since the typical approach to this problem requires optimizing over a space that is exponential in the number of links, the problem has appeared to be computationally intractable for all but small networks. In this paper, the problem of computing optimal bandwidth allocation is examined and a new approach is presented. While the resulting allocation cannot be guaranteed to be optimal, we find that in the networks where checking optimality is computationally feasible (i.e., networks with fewer than 23 links), the performance of the found allocation is indistinguishable from the optimal allocation. In essence, the proposed iterative scheme focuses on the space of useful bandwidth allocations. The Lagrange multipliers are used to find useful allocations.