—The problem of minimum cost in-network fusion of measurements, collected from distributed sensors via multihop routing is considered. A designated fusion center performs an optimal statistical-inference test on the correlated measurements, drawn from a Markov random field. Conditioned on the delivery of a sufficient statistic for inference to the fusion center, the structure of optimal routing and fusion is shown to be a Steiner tree on a transformed graph. This Steiner-tree reduction preserves the approximation ratio, which implies that any Steinertree approximation can be employed for minimum cost fusion with the same approximation ratio. The proposed fusion scheme involves routing packets of two types viz., raw measurements sent for local processing, and aggregates obtained on combining these processed values. The performance of heuristics for minimum cost fusion are evaluated through theory and simulations, showing a significant saving in routing costs, when compared to routi...