Step 10: The LP solution is all 0's and 1's. In such a case we either have a tour, or the solution splits up into islands. Unfortunately, in our example we do in fact have two islands. We will add the subtour-elimination constraint for cities in the bottom island; the set S consists of the cities 0 through 12.
Note that we are paying the price for not including city 12 in the previous subtour-elimination constraint, but if we had included 12, the constraint for 0 through 11 would probably be violated at this step.
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