In this paper, we study the performance of greedy scheduling in multihop wireless networks, where the objective is aggregate utility maximization. Following standard approaches, we consider the dual of the original optimization problem. The dual can
be solved optimally, only with the knowledge of the maximal independent sets in the network. But computation of maximal independent sets is known to be NP-hard. Motivated by this, we propose a distributed greedy heuristic to address the problem of link scheduling. We evaluate the effect of the distributed greedy heuristic on aggregate utility maximization in detail, for the case of an arbitrary graph. We provide some insights into the factors affecting aggregate utility maximization in a network, by providing bounds on the same. We give simulation results for the approximate aggregate utility maximization achieved under distributed implementation of the greedy heuristic and find them close to the maximum aggregate utility obtained using optimal scheduling.
