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We propose in this work a single copy and multi-hop opportunistic routing scheme for sparse delay tolerant networks (DTNs). The scheme uses as only input the estimates of the average inter-contact times between the nodes in the network. Defined as the fixed point of a recursive process, it aims at minimizing delivery time in case of independent exponential pairwise inter-contacts. The two properties of loop-free forwarding and polynomial convergence make the scheme workable for routing in DTNs. The routing performances of the scheme are evaluated on three publicly available reference data sets. Comparisons with well known single-copy schemes, including MED and the two hop relay strategy, consistently demonstrate improvements for both delivery ratio and delay.