发表机构
University of Nebraska-Lincoln; Rensselaer Polytechnic Institute; Beijing Normal University-Zhuhai（内布拉斯加大学林肯分校; 伦斯勒理工学院; 北京师范大学珠海校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对战略厌恶型设施选址问题，提出改进的随机策略证明机制，分别将社会效用和最小效用的近似比优化至1.47359和√n+O(1)，并提高下界至105/88和2。
AI 中文摘要
我们研究了线段上战略厌恶型设施选址的随机策略证明机制，其中智能体希望设施尽可能远离他们，其效用是距设施的距离，目标分别为社会效用和最小效用。对于社会效用，我们提出了一种新颖的随机机制，打破了先前已知的[Cheng, Yu, and Zhang, TCS 2013]中的3/2近似比，实现了至多1.47359的近似比。我们还将随机策略证明机制的近似比下界从[Feigenbaum et al., JAAMAS 2020]中的2/√3≈1.15470提高到105/88≈1.19318。对于最小效用，遵循[Chan, Lin and Wang, AAMAS 2026]的与轮廓无关的方法，我们设计了一种简单的随机机制，将近似保证从√(2n)+O(1)降低到√n+O(1)，其中n是智能体数量。最后，我们证明了没有任何随机策略证明机制能够实现严格小于2的渐近近似比，加强了先前[Feigenbaum et al., JAAMAS 2020]中3/2的渐近下界。因此，本文考虑的所有四个界限都严格优于相应的先前已知结果。
英文摘要
We study randomized strategyproof mechanisms for strategic obnoxious facility location on a line segment, where agents wish the facility to be located as far away from them as possible and their utility is their distance from the facility, under the social utility and minimum utility objectives. For social utility, we propose a novel randomized mechanism that breaks the previously best known \(\frac32\)-approximation of [Cheng, Yu, and Zhang, TCS 2013], achieving an approximation ratio of at most \(1.47359\). We also raise the lower bound on the approximation ratio of randomized strategyproof mechanisms from \(\frac{2}{\sqrt{3}}\approx1.15470\) [Feigenbaum et al., JAAMAS 2020] to \(\frac{105}{88}\approx1.19318\). For minimum utility, following the profile-independent approach of [Chan, Lin and Wang, AAMAS 2026], we design a simple randomized mechanism that reduces the approximation guarantee from \(\sqrt{2n}+O(1)\) to \(\sqrt n+O(1)\), where \(n\) is the number of agents. Finally, we prove that no randomized strategyproof mechanism can achieve an asymptotic approximation ratio strictly smaller than \(2\), strengthening the previous asymptotic lower bound of \(\frac32\) [Feigenbaum et al., JAAMAS 2020]. Thus, all four bounds considered in this paper strictly improve upon the corresponding previously known results.
CommentsTo appear in ISAAC 2026
