12.4 Is the following a theorem: An approximation algorit hm designed using an LP-relaxation cannot achieve a better approxim 12.4 Is the following a theorem: An approximation algorit hm designed using an LP-relaxation cannot achieve a better approximation guarantee than the integrality gap of the relaxation Hint: In principle it may be possible to show, using additional structural properties, that whenever an instance has a bad gap, the cost of the solution found by the algorithm is much less that aOPT, where a is the integrality gap of the relaxation. (Observe that if the instance has a bad gap, the cost of the solution found cannot be much less than aOPTf.)



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