(Figure omitted because of lack of space.)
The original decision problem now has answer ``yes'' if and only if there is a subset such that c(S) = 0.
Implement, on your favorite computer system, one of the following three methods to solve this problem for a given fixed value of n: (a) iterated local search (from randomly chosen initial solutions), (b) simulated annealing, (c) some variety of genetic algorithm. Experiment with different parameter settings.