ABSTRACT In this paper, we study the problem of vector scheduling with rejection on two identical parallel machines, where the objective is to minimize the sum of maximum load over all dimensions and machines and the total penalty cost. We present a 3-approximation algorithm and a 2.54-approximation algorithm based randomized rounding for the general case. When the number of dimensions is fixed, we design a fully polynomial time approximation scheme based on dynamic programming. Finally, we design an online algorithm with competitive ratio 1.62d, where d is the number of dimensions.

中文翻译：

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两台机器上带有拒绝的向量调度

摘要在本文中，我们研究了在两台相同的并行机器上拒绝向量调度的问题，其目标是最小化所有维度和机器上的最大负载和总惩罚成本的总和。我们针对一般情况提出了基于随机舍入的 3 近似算法和 2.54 近似算法。当维数固定时，我们设计了一个基于动态规划的完全多项式时间近似方案。最后，我们设计了一个竞争比为 1.62d 的在线算法，其中 d 是维数。