For the Routing Open Shop problem with unit execution times, the first algorithm with parameterized complexity is designed for constructing an optimal schedule. Its running time is bounded by a function (Pol(|V |) + f(m, g))·|I|, where Pol(|V|) is a polynomial of the number of network nodes, f(m, g) is a function of the number of machines and the number of job locations, and |I| is the input length in its compact encoding.
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