最小完工时间补全与顶点选择使 Wang-Sitters 常数保持为 11/6
Minimum-makespan completion and vertex selection leave the Wang-Sitters constant at 11/6
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中文总结 AI 辅助
本文证明消除 Wang-Sitters 舍入方案第 3 步自由度不改进其 11/6 最坏情况常数，最小完工时间补全与顶点选择均无效，并记录存留结构及严格 7/4 界。
中文摘要 AI 辅助
Wang-Sitters 舍入方案的最坏情况常数 11/6（由配套注释确立）可自然地归因于第 3 步中的自由度，其中允许任意有效的槽位匹配。我们证明消除该自由度并不能改善该常数。最小完工时间补全预言机相对于最优解的最坏情况常数仍恰好为 11/6；关于它的两个自然的 7/4 命题均为假；将第 1 步限制为松弛的顶点也无济于事。因此，损失不能仅归因于第 3 步的自由度。我们还记录了存留的结构：将每个过载限制为两种形状的约简、击败自然两阶段修复的七机器实例，以及广义三路径族上的严格 7/4 界。
英文摘要
The 11/6 worst-case constant of the Wang-Sitters rounding scheme, which a companion note establishes, can naturally be attributed to the freedom in Step 3, where an arbitrary valid slot matching is permitted. We show that eliminating that freedom does not improve the constant. A minimum-makespan completion oracle still has worst-case constant exactly 11/6 against the optimum; both natural 7/4 statements about it are false; and restricting Step 1 to vertices of the relaxation does not help. The loss therefore cannot be attributed solely to the freedom in Step 3. We also record what structure survives: a reduction confining every overload to two shapes, a seven-machine instance defeating the natural two-phase repair, and a strict 7/4 bound on the generalized three-path family.
发表机构
- Hunter College and the Graduate Center, CUNY（亨特学院和纽约市立大学研究生中心）
机构由 AI 辅助整理，请以论文原文为准。
