Gap reduction

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In computational complexity theory, a gap reduction is a reduction to a particular type of decision problem, known as a c-gap problem. Such reductions provide information about the hardness of approximating solutions to optimization problems. In short, a gap problem refers to one wherein the objective is to distinguish between cases where the best solution is above one threshold from cases where the best solution is below another threshold, such that the two thresholds have a gap in between. Gap reductions can be used to demonstrate inapproximability results, as if a problem may be approximated to a better factor than the size of gap, then the approximation algorithm can be used to solve the corresponding gap problem.