An approach for cell routing using gridded design rules is proposed. It is technology-independent and parameterizable for different fabrics and design rules, including support for multiple-patterning lithography. The core contribution is a detailed-routing algorithm based on a Boolean formulation of the problem. The algorithm uses a novel encoding scheme, graph theory to support floating terminals, efficient heuristics to reduce the computational cost, and minimization of the number of unconnected pins in case the cell is unroutable. The versatility of the algorithm is demonstrated by routing single-and double-height cells. The efficiency is ascertained by synthesizing a library with 127 cells in about one hour and a half of CPU time. The layouts derived by the implemented tool have also been compared with the ones from a commercial library; thus, showing the competitiveness of the approach for gridded geometries.