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Complementary trees are two spanning trees rooted at the sink node satisfying that any source node's two paths to the sink node on the two trees are node-disjoint. Complementary trees routing strategy is a special node-disjoint multi-path routing approach. Several complementary trees routing algorithms have been proposed, in which path discovery methods based on depth first search (DFS) or Dijkstra's algorithm are used to find a path for augmentation in each round of path augmentation step. In this paper, a novel path discovery method based on multi-tree-growing (MTG) is presented for the first time to our knowledge. Based on this path discovery method, a complementary trees routing algorithm is developed with objectives of low average path length on both spanning trees and low complexity. Measures are employed in our complementary trees routing algorithm to add a path with nodes near to the sink node in each round of path augmentation step. The simulation results demonstrate that our complementary trees routing algorithm can achieve low average path length on both spanning trees with low running time, suitable for wireless sensor networks in industrial scenarios.