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Some voting schemes that are in principle susceptible to control are nevertheless resistant in practice due to excessive computational costs; others are vulnerable. We illustrate this in detail for plurality voting and for Condorcet voting.

We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branch-and-bound tree. This approach, while requiring the solution of a di cult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. We have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented.

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