The article studies the problem of designing telecommunication networks using transmission facilities of two different capacities. The point‐to‐point communication demands are met by installing a mix of facilities of both capacities on the edges to minimize total cost. We consider 3‐partitions of the original graph which results in smaller 3‐node subproblems. The extreme points of this subproblem polyhedron are characterized using a set of propositions. A new approach for computing the facets of the 3‐node subproblem is introduced based on polarity theory. The facets of the subproblem are then translated back to those of the original problem using a generalized version of a previously known theorem. The approach has been tested on several randomly generated and real life networks. The computational results show that the new family of facets significantly strengthen the linear programming formulation and reduce the integrality gap. Also, there is a substantial reduction in the size of the branch‐and‐bound (B&B) tree if these facets are used. Problems as large as 37 nodes and 57 edges have been solved to optimality within a few minutes of computer time. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(1), 11–32 2015

International audienceIn this paper, we study the problem of resource allocation in SC-FDMA systems. A sum-utility maximization is considered where the utility of each user may be neither additive nor super additive. Unlike OFDMA, in addition to the restriction of allocating a subchannel to at most one user, the multiple subchannels allocated to a user in SC-FDMA must be consecutive. This makes the resource allocation problem prohibitively difficult and challenging. We provide a fundamental complexity analysis of the optimization problem for general non-additive utility functions and show that not only the problem is NP-hard but also approximating it within a factor better than $ {{2011}over {2012}}$ is not possible unless ${rm P}={rm NP}$. An efficient cutting plane algorithm is presented and five suboptimal heuristics are also presented that achieve near optimal solution in different scenarios. Computational results of the cutting plane and heuristic algorithms are reported and a comparison between these heuristics is provided as well

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