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In this paper, we propose a novel on-demand routing protocol for IEEE 802.15.4-based low rate wireless mesh networks (LRWMNs). The novelty of our work is that the proposed routing algorithms enable route discovery packets (RREQs) to be semi-directionally flooded with respect to a source-destination pair in a distributed manner without either physical or virtual location systems. Instead, we use the logical tree distance derived from the hierarchical addressing structure. The idea behind this is that nodes with longer tree distance to the destination than that of the source-destination pair are not involved in flooding RREQs. To evaluate the algorithms, we apply our algorithms into AODVjr and carry out extensive simulations while comparing the algorithms with AODVjr using network-wide flooding (NWF). Results show that the proposed algorithms drastically reduce RREQ overhead while providing comparable or better performance than NWF in AODVjr.