From 2007.igem.org

This graph above shows a modified complete graph with edges leaving the ending node (#4), returning to the start node (#1), and moving from the start to the stop node removed. If we wanted to solve this weighted and directed graph for the shortest path through all nodes, starting at node #1, ending at node #4, and passing through each node only once, we could use our current HPP E. coli computer construct with one slight modification.

Instead of putting each half-gene back to back along an edge, we could add in spacers of specified lengths that would allow us to model the various weights in the graph above. These weights would give edges different lengths (in base pairs). After performing PCR on all of the solved plasmids (with primers binding to the promoter and terminator), we would be able to find the shortest path through all of the nodes by running the PCR products on a gel. The smallest fragment will be the solution to the Traveling Salesperson Problem.