基于Copula的两台不相关机器真实排序的随机机制
Copula-based Randomized Mechanisms for Truthful Scheduling on Two Unrelated Machines
摘要：
我们设计了一个基于Copula的通用随机真实机制，用于两台不相关机器上的调度，近似比在$[1.5852, 1.58606]$内，为两台机器的情况提供了一个改进的上界。此外，我们为两台机器两个任务的情况提供了一个上限1.5067711，鉴于无标度真实机制的下限1.506，这几乎是紧的[4]。独立的利益是明确纳入Copula的概念，在设计和分析所提出的近似算法。我们希望像这样的技术也能被证明对解决未来的其他问题有用。
英文摘要：
We design a Copula-based generic randomized truthful mechanism for scheduling on two unrelated machines with approximation ratio within $[1.5852, 1.58606]$, offering an improved upper bound for the two-machine case. Moreover, we provide an upper bound 1.5067711 for the two-machine two-task case, which is almost tight in view of the lower bound of 1.506 for the scale-free truthful mechanisms [4]. Of independent interest is the explicit incorporation of the concept of Copula in the design and analysis of the proposed approximation algorithm. We hope that techniques like this one will also prove useful in solving other problems in the future.
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