In 1994, Frieze and Teng proposed an integer linear programming formulation of the NP-Complete Exact Partition problem, whose LP-relaxation they claimed was non-degenerate. Contrary to their claim, we show how an instance of Exact Partition can produce a degenerate polytope, and study conditions for which this can happen. We then give details of one of the smallest such degenerate Frieze-Teng polytopes, along with a closely related non-degenerate Frieze-Teng polytope that encodes an equivalent problem. We note that for the purposes of the complexity results in the literature that use their formulation, these degenerate polytopes can be avoided via a simple preprocessing step.

翻译：1994年，Frieze和Teng针对NP完全的精确划分问题提出了一种整数线性规划形式，并声称其LP松弛是非退化的。与他们声称相反，我们展示了精确划分的实例如何产生退化多面体，并研究了导致此现象的条件。随后，我们详细描述了其中一个最小的此类退化Frieze-Teng多面体，以及一个编码等价问题的密切相关的非退化Frieze-Teng多面体。我们指出，在利用其形式的文献复杂性结果中，可通过简单的预处理步骤避免这些退化多面体。