On internal-external layouts

E.L. Lloyd and S.S. Ravi recently (1984) considered the problem of writing in a channel using one layer. They restricted their investigation to the river-routing problem and defined two classes of layouts, fully internal and internal-external layouts. The approach of internal-external layout is more powerful and it can solve problems more generally than the river-routing problem. Determining the conditions under which an arbitrary channel routing problem admits an internal-external layout is mentioned as an interesting open problem. A complete characterization of channel routing problems that admit an internal-external layout is presented, and a linear-time algorithm for testing if a channel routing problem admits such a layout is proposed