Online contention resolution schemes (OCRSs) are effective rounding techniques for online stochastic combinatorial optimization problems. These schemes randomly and sequentially round a fractional solution to a relaxed problem that can be formulated in advance. We propose OCRSs for online stochastic generalized assignment problems. In the OCRSs problem, sequentially arriving items are packed into a single knapsack, and their sizes are revealed only after insertion. The goal of the problem is to maximize the acceptance probability, which is the smallest probability among the items of being placed in the knapsack. Since the item sizes are unknown beforehand, a capacity overflow may occur. We consider two distinct settings: the hard constraint, where items that cause overflow are rejected, and the soft constraint, where such items are accepted. Under the hard constraint setting, we present an algorithm with an acceptance probability of $1/3$, and we also prove that no algorithm can achieve an acceptance probability greater than $3/7$. Under the soft constraint setting, we propose an algorithm with an acceptance probability of $1/2$, and we show that this is best possible.

翻译：在线竞争解决机制（OCRSs）是面向在线随机组合优化问题的有效舍入技术。这些机制对预先制定的松弛问题的分数解进行随机顺序舍入。本文针对在线随机广义分配问题提出了OCRSs方案。在该OCRSs问题中，依次到达的物品被装入单个背包，其尺寸仅在装入后才会显现。问题的目标是最大化接受概率，即各物品被放入背包的最小概率。由于物品尺寸事先未知，可能出现容量溢出。我们考虑了两种不同的约束设置：硬约束（导致溢出的物品被拒绝）和软约束（此类物品被接受）。在硬约束设置下，我们提出了一种接受概率为$1/3$的算法，并证明没有任何算法的接受概率能超过$3/7$。在软约束设置下，我们提出了一种接受概率为$1/2$的算法，并证明这是最优可达值。