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Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose "disassembly and assembly of a graph" algorithm which uses a solution of the problem on a small-dimensional graph to obtain the solution for the given graph. The proposed algorithm has been compared to one of the fastest classic algorithms on data from an open public source.doi:10.13189/csit.2013.010309 fatcat:eszaf64d4jf4hliayvt7mv6nom