The Matou\v{s}ek LP-type problems were used by Matou\v{s}ek to show that the Sharir-Welzl algorithm may require at least subexponential time. Later, G\"artner translated this result into the language of Unique Sink Orientations (USOs) and introduced the Matou\v{s}ek USOs, the USOs equivalent to Matou\v{s}ek's LP-type problems. He further showed that the Random Facet algorithm only requires quadratic time on the realizable subset of the Matou\v{s}ek USOs, but without characterizing this subset. In this paper, we deliver this missing characterization and also provide concrete realizations for all realizable Matou\v{s}ek USOs. Furthermore, we show that the realizable Matou\v{s}ek USOs are exactly the orientations arising from simple extensions of cyclic-P-matroids.
翻译：Matou\ v{s}k LP 类型问题被Matou\ v{s}ek用来表明 Sharir- Welzl 算法至少需要亚化时间。 后来, G\\\ “ artner” 将这一结果翻译为独特 Sink 方向 (USOs) 的语言, 并引入了 Matou\ v{s}ek USOs, 相当于 Matou\ v{s}ek 的LP 类型问题 。 他进一步显示 随机 Facet 算法仅需要可变现的 Matou\ v{s}ek USOs 子集中的二次时间, 但不对子集定性 。 在本文中, 我们提供这一缺失的特性, 并为所有可变现的 Matou\ v{s}ek USOs 提供具体实现效果。 此外, 我们显示可变现的 Matou\ v{s} USOs 正是由周期- P-matroids 简单扩展产生的方向 。
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