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In this paper, two novel distributed routing schemes, named adaptive-information-moving-rate routing scheme (AIMR) and adaptive-information-moving-distance-and-link-rate routing scheme (AIMDLR), are proposed for multi-hop wireless networks by jointly considering the number of hops and the link states. With one-hop information only, both schemes aim at improving the network spectral efficiency under two different bandwidth sharing methods (i.e., throughput-maximization bandwidth sharing and equal-time bandwidth sharing), respectively. In addition, a general scheme, called probability-based scheme (PBS), is proposed to improve the accessibility of distributed routing schemes, which is denoted by the success probability of finding a route reaching the destination. In the PBS, the node selection in each hop is based on a well-defined probability, which takes into account the locations of the transmitter and the receiver at each hop and the uncertainty in the subsequent hops. By combining the PBS with the AIMR and the AIMDLR, the proposed probability-based AIMR (PAIMR) and probability-based AIMDLR (PAIMDLR) can not only improve the accessibility significantly but also achieve higher effective spectral efficiency compared to the counterparts. Simulation results are finally presented to demonstrate the advantages of the proposed routing schemes.