发表机构
Université Grenoble Alpes, Grenoble INP, CNRS, INRIA, LIG（格勒诺布尔阿尔卑斯大学、格勒诺布尔理工学院、法国国家科学研究中心、法国研究与计算机科学研究所、信息学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对欧氏空间的战略设施选址问题，利用额外维度优化防策略机制，得出了高维空间近似因子下界并改进了平面及带额外维度场景的算法。
AI 中文摘要
战略设施选址问题定义如下：n个智能体在度量空间中报告其位置，目标是设计一种机制来决定设施的（可能是随机的）位置，使得智能体没有动机谎报自身位置。我们关注平等成本，即机制的目标是最小化设施与智能体之间的期望最大距离。同时，机制必须是真实的（或防策略的）：没有智能体可以通过谎报位置来降低其到设施的期望距离。设计最小化近似比的真实机制是一个被广泛研究的问题，对于实数直线上的情况，最优解是已知的。本文中我们关注更高维度的欧氏空间，在该空间中，已知的上下界之间仍存在差距。我们首先证明，可能与直觉相反，平面上两个智能体的该问题比直线上的更简单：机制可以利用额外维度更有效地防止智能体谎报。基于这一直觉，我们为ℝᵈ得出了渐近匹配已知最佳近似因子2的下界（针对大d的情况）。我们还提出了新的机制思路，改进了平面上已知的最佳算法，以及当智能体属于ℝᵈ但设施可使用额外维度时的情况。
英文摘要
The strategic facility location problem is defined as follows: $n$ agents report their location in a metric space, and the objective is to design a \emph{mechanism} deciding the (possibly randomized) location of a facility such that agents have no incentive to lie about their position. We focus on the egalitarian cost, which means that the goal of the mechanism is to minimize the expected maximal facility-agent distance. Meanwhile, mechanisms must be \emph{truthful} (or \emph{strategyproof}): no agent may decrease their expected distance to the facility via lying on their location. Designing truthful mechanisms minimizing the approximation ratio is a well-studied problem, and the optimal solution is known for the real line. We focus in this paper on higher dimension Euclidean spaces, for which gaps remain between the best known lower and upper bounds. We first show that, maybe counter-intuitively, the problem is easier for two agents on the plane rather than on the line: the mechanism can exploit the additional dimension to prevent more efficiently agent lies. Based on this intuition, we devise lower bounds for $\mathbb R^d$ asymptotically matching the best known approximation factor of $2$ for large $d$. We also provide novel mechanism ideas, improving over the best known algorithms on the plane, and when the agents belong to $\mathbb R^d$ but the facility may use an additional dimension.
