Giving a set of integer we want to know whether it is possible to partition this set of integers into two sub-sect, such that the sum of the integers contained in one sub-sect is equal to the sum of the integers contained in the other sub-sect. This problem is a NP-complete and we can reduce it to bin packing in the following way. Given an instance I we derive a new instance for bin packing for by I and B, where B is equal half of the total sum of the integers. We have that if I is a positive instance, then the measure of the optimal solution of the instance is equal to 2, otherwise if I is not a positive instance then the measure of the optimal solution of the instance must be at least 3. Since 3 can be written as 2(1+1/2) this means that we have a gap equal to 1/2. This implies that the minimum bin packing has no r-approximation algorithm with r<3/2, unless P=NP.

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