The distributed short-path set (DSS) of an origin-destination (OD) pair in a network is a set that consists of multiple paths from the O node to the D node, which have lengths close to the shortest path length, and share less overlap between each other. In this brief, we propose a high-efficiency algorithm to calculate the DSSs for networks, named as the diffusional DSS algorithm (DDSSA). The results based on extensive computer simulations on typical complex networks show that DDSSA calculates high-quality DSSs in short time, and well supports the distributed multiple short-paths (DMS) routing, which is designed to select a lowest-cost routing path for each transmission task from the DSS of its OD pair with respect to the network transmission status information (NTSI). Further study shows that, the delay of NTSI wakens the transmission performance improvement raised by the DMS routing, and largely delayed NTSI may worsen the performance when overmuch distributed short-paths are provided or a multiple-assign strategy is employed.