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We present an optimal distributed algorithm to adapt the placement of a single operator in high communication cost networks, such as a wireless sensor network. Our parameter-free algorithm finds the optimal node to host the operator with minimum communication cost overhead. Three techniques, proposed here, make this feature possible: 1) identifying the special, and most frequent case, where no flooding is needed, otherwise 2) limitation of the neighborhood to be flooded and 3) variable speed flooding and eves-dropping. When no flooding is needed the communication cost overhead for adapting the operator placement is negligible. In addition, our algorithm does not require any extra communication cost while the query is executed. In our experiments we show that for the rest of cases our algorithm saves 30%-85% of the energy compared to previously proposed techniques. To our knowledge this is the first optimal and distributed algorithm to solve the 1-median (Fermat node) problem.