Field-programmable gate arrays (FPGAs) can be used effectively to emulate complex digital systems. This paper is concerned with their use in the emulation of complex digital designs. In a previous paper [1], the authors showed that the board-level routing problem is NP-complete, and they now show how a relaxation of constraints can make the problem solvable. A network flow–based algorithm is given in pseudocode form, and three lemmas establish its viability. The paper ends with a table that shows the result of practical experiments with the method.