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In this paper, the authors consider a heterogeneous network with one macro node and one pico node. They are concerned with the problem of associating users in the macro cell, to either the macro node or the pico node, in order to maximize the sum rate in the downlink. They formulate a new theoretical framework to study this problem and derive an upper bound on the achievable sum rate using semidefinite relaxation. Furthermore, they propose a randomized heuristic to produce a feasible solution, and most importantly, give an analytic guarantee on its performance. Independently of the problem data, they can ensure a worst case performance for the randomization method.
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