This paper re-examines the problem of fairly and efficiently allocating indivisible goods among agents with additive bivalued valuations. Garg and Murhekar (2021) proposed a polynomial-time algorithm that purported to find an EFX and fPO allocation. However, we provide a counterexample demonstrating that their algorithm may fail to terminate. To address this issue, we propose a new polynomial-time algorithm that computes a WEFX (Weighted Envy-Free up to any good) and fPO allocation, thereby correcting the prior approach and offering a more general solution. Furthermore, we show that our algorithm can be adapted to compute a WEQX (Weighted Equitable up to any good) and fPO allocation.

翻译：本文重新审视了在具有可加性双值估值的情况下，将不可分割物品公平高效地分配给智能体的问题。Garg与Murhekar (2021) 曾提出一个多项式时间算法，声称可以找到EFX且fPO的分配方案。然而，我们提供了一个反例，证明他们的算法可能无法终止。为解决此问题，我们提出了一种新的多项式时间算法，能够计算出WEFX（加权无嫉妒至任意物品）且fPO的分配方案，从而修正了先前的方法，并给出了一个更通用的解决方案。此外，我们证明该算法可被调整以计算WEQX（加权公平至任意物品）且fPO的分配方案。