发表机构
Institute of Computing, University of Campinas; Institute of Mathematics, Statistics and Computer Science, University of São Paulo（坎皮纳斯大学计算研究所; 圣保罗大学数学、统计和计算机科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种精简双列表算法，并证明紧致占用面积界，将动态二维正方形装箱的渐近竞争比上界从4.2154降至3.918，并给出单位分数和幂分数边长变体的改进上界。
AI 中文摘要
本文针对动态二维正方形装箱问题提出了显著的上界改进，其中正方形物品随时间到达和离开，目标是最小化并发活动单位箱的峰值数量。在我们的模型中，仅允许在物品到达时在目标箱内进行重新打包；活动箱之间的迁移被严格禁止。通过引入一种精简的双列表算法，并证明 Next-Fit Decreasing Height 的紧致 $5/16$ 占用面积界，我们将任意正方形的渐近竞争比上界从 4.2154 降低到 3.918，打破了长期存在的理论天花板。对于受限变体，我们建立了单位分数边长渐近竞争比至多 3.356，幂分数边长至多 2.211 的结果。
英文摘要
This paper presents significant upper-bound improvements for dynamic 2D square bin packing, where square items arrive and depart over time and the objective is to minimize the peak number of concurrent active unit bins. In our model, repacking is permitted only within a destination bin upon item arrival; migration between active bins is strictly forbidden. By introducing a streamlined two-list algorithm and proving a tight $5/16$ occupied-area bound for Next-Fit Decreasing Height, we reduce the upper bound on the asymptotic competitive ratio for arbitrary squares from 4.2154 down to 3.918, breaking a longstanding theoretical ceiling. For restricted variants, we establish asymptotic competitive ratios of at most 3.356 for unit-fraction side lengths and 2.211 for power-fraction side lengths.
Comments20 pages, 2 figures
