In a V-vertex E-edge graph... What string-machine salesman Lunnon forgot to say, is that enormous edge-length integers, N bits long, would require an exponentially large budget to purchase the string, plus the thing would gravitationally collapse into a black hole. If the edge lengths were selected from a BOUNDED set of integers only, though, then Lunnon's "string machine" for all shortest paths would work... it takes O(E+V) steps to build it, then to solve the A-B shortest path problem requires effort (force, energy expenditure versus friction, also time if you have bounded power source) of order O(E+V) to pull on that much weight. Meanwhile the conventional computer has a linear time algorithm O(V+E) for single source, all destinations, shortest paths (assuming bounded nonnegative integer edge lengths), then constant time lookups... so, sorry, Lunnon+string has not really beat conventional computers. A nicer try was made by Ken Steiglitz who once invented a machine made of rigid parts to solve NP-complete problems instantly. (Some part can move, or not, if the SAT problem has solution, or not.) Really, though, it won't work, albeit the physical reasons for the failure are a bit subtle and were not understood by KS himself.