Relaxation of 3-partition instances
نویسندگان
چکیده
The 3-partition problem admits a straightforward formulation as a 0-1 Integer Linear Program (ILP). We investigate problem instances for which the half-integer relaxation of the ILP is feasible, while the ILP is not. We prove that this only occurs on a set of at least 18 elements, and in case of 18 elements such an instance always contains an element of weight ≥ 10. These bounds are sharp: we give all 14 instances consisting of 18 elements all having weight ≤ 10. Our approach is based on analyzing an underlying graph structure.
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