在线装箱问题中的每箱最大延迟

中文摘要 AI 辅助

我们研究具有每箱最大延迟的在线装箱问题：每个密封箱产生单位开启成本加上其物品中最长的等待时间。离线情况下，这成为一个时间跨度装箱目标。我们证明了强NP困难性，并排除了低于二分之三的绝对近似因子，除非P等于NP。我们通过多项式常数因子近似、若干特殊情况的精确算法以及固定长度加权端点子问题的AFPTAS来补充这些障碍。对于对抗性在线输入，我们在理想随机实数模型中给出了一种高效的随机算法，其预期竞争比约为2.418，对抗不知情对手，同时给出确定性和随机性下界。其分析将Next-Fit碎片化与由静默簇产生的负信用相结合。当容量不受约束时，两个前沿问题都被精确解决。我们还为泊松到达且每个物品具有箱容量一半的情况获得了精确的随机基准：我们刻画了离线速率，确定了最优因果策略，并表明两个自然的渐近比率概念一致且有界于三分之四。

英文摘要

We study online bin packing with per-bin maximum delay: each sealed bin incurs a unit opening cost plus the longest waiting time among its items. Offline, this becomes a temporal-span packing objective. We prove strong NP-hardness and rule out absolute approximation factors below three halves unless P equals NP. We complement these barriers with a polynomial constant-factor approximation, exact algorithms for several special cases, and an AFPTAS for the fixed-length weighted endpoint subproblem. For adversarial online inputs, we give an efficient randomized algorithm in the ideal random-real model with expected competitive ratio about 2.418 against an oblivious adversary, together with deterministic and randomized lower bounds. Its analysis couples Next-Fit fragmentation to a negative credit generated by silence clusters. Both frontiers are solved exactly when capacity is nonbinding. We also obtain an exact stochastic benchmark for Poisson arrivals when every item has half the bin capacity: we characterize the offline rate, identify an optimal causal policy, and show that two natural asymptotic ratio notions agree and are bounded by four thirds.

发表机构

• Southern University of Science and Technology（南方科技大学）

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