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This paper considers the problem of energy-efficient transmission inmulti-flow multihop cooperative wireless networks. Although the performancegains of cooperative approaches are well known, the combinatorial nature ofthese schemes makes it difficult to design efficient polynomial-time algorithmsfor joint routing, scheduling and power control. This becomes more so whenthere is more than one flow in the network. It has been conjectured by manyauthors, in the literature, that the multiflow problem in cooperative networksis an NP-hard problem. In this paper, we formulate the problem, as acombinatorial optimization problem, for a general setting of $k$-flows, andformally prove that the problem is not only NP-hard but it is$o(n^{1/7-\epsilon})$ inapproxmiable. To our knowledge*, these results providethe first such inapproxmiablity proof in the context of multiflow cooperativewireless networks. We further prove that for a special case of k = 1 thesolution is a simple path, and devise a polynomial time algorithm for jointlyoptimizing routing, scheduling and power control. We then use this algorithm toestablish analytical upper and lower bounds for the optimal performance for thegeneral case of $k$ flows. Furthermore, we propose a polynomial time heuristicfor calculating the solution for the general case and evaluate the performanceof this heuristic under different channel conditions and against the analyticalupper and lower bounds.

Multiflow Transmission in Delay Constrained Cooperative Wireless Networks