In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution quality. It uses the max-sum algorithm to optimally solve the resulting tree structured constraint network, providing a bounded approximation specific to the particular problem instance. We formally prove that our algorithm provides a bounded approximation of the original problem and we present an empirical evaluation in a synthetic scenario. This shows that the approximate solutions that our algorithm provides are typically within 95% of the optimum and the approximation ratio that our algorithm provides is typically 1.23.