An algorithm with parameterized complexity of constructing the optimal schedule for the routing open shop problem with unit execution times. van Bevern, R. A., Pyatkin, A. V., & Sevastyanov, S. V. Siberian Electronic Mathematical Reports, 16:42–84, 2019.
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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.
@article{BPS19,
  author =	 {René A. van Bevern and Artem V. Pyatkin and Sergey
                  V. Sevastyanov},
  journal =	 {Siberian Electronic Mathematical Reports},
  title =	 {An algorithm with parameterized complexity of
                  constructing the optimal schedule for the routing
                  open shop problem with unit execution times},
  date =	 {2019-01-27},
  year =	 2019,
  volume =	 16,
  pages =	 {42--84},
  doi =		 {10.33048/semi.2019.16.003},
  issn =	 {1813-3304},
  abstract =	 {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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