发表机构
University of Nebraska-Lincoln; Rensselaer Polytechnic Institute; Beijing Normal University-Zhuhai; Beijing Normal-Hong Kong Baptist University（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; 北京师范大学-香港浸会大学联合国际学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对线段上被障碍物分隔区域的路径建设问题，提出策略性机制，实现最大成本紧近似比2/(1+k)及社会成本上界，并改进随机机制界。
AI 中文摘要
我们研究在一条线段上被障碍物分隔的两个区域之间建立路径的策略性机制。每个n个智能体在其所在区域内拥有一个私有位置，并且可以使用其到设施的原始路线或新路径，新路径的通行成本是其长度的分数k∈[0,1)。我们寻求策略性（SP）和群体策略性（GSP）机制，以近似最小化最大成本或社会成本。在刻画了两种目标的最优路径之后，我们建立了最大成本的紧确定性近似比为2/(1+k)，以及社会成本的确定性上界为n/(1+k(n-1))，并给出了相应的下界。两个上界均由GSP机制实现。然后，我们研究了在期望策略性下的随机机制。一个功率比例机制实现了至多5的社会成本近似比，与n和k无关，并且当k=0时该机制具有紧的保证3。我们证明了最大成本的随机下界为(3+2k)/(2+3k)，社会成本的随机下界为max{1, 285/(263+385k)}，后者适用于n≥7。最后，我们改进了[Chan and Wang, AAMAS 2023]的实线路径模型的几个界。我们的最大成本确定性下界2与[Qin, Fang, and Liu, COCOA 2024]可获得的上界相匹配。我们将社会成本的确定性下界从3/2加强到SP下的2和GSP下的max{2, n-1}。对于随机社会成本，我们将Chan和Wang的比例机制的保证从6改进到3，并将其下界从1.02提高到n≥7时的285/263≈1.08365。
英文摘要
We study strategyproof mechanisms for building a pathway between two regions of a line segment separated by an obstacle. Each of the $n$ agents has a private location within its region and may use either its original route to a facility or the new pathway, whose traversal cost is a fraction $k\in[0,1)$ of its length. We seek strategyproof (SP) and group-strategyproof (GSP) mechanisms that approximately minimize maximum cost or social cost. After characterizing optimal pathways for both objectives, we establish a tight deterministic maximum-cost approximation ratio of $\frac{2}{1+k}$ and a deterministic social-cost upper bound of $\frac{n}{1+k(n-1)}$, together with complementary lower bounds. Both upper bounds are achieved by GSP mechanisms. We then study randomized mechanisms under strategyproofness in expectation. A power-proportional mechanism achieves a social-cost approximation ratio at most $5$, independent of $n$ and $k$, with a tight guarantee of $3$ for this mechanism when $k=0$. We prove randomized lower bounds of $\frac{3+2k}{2+3k}$ for maximum cost and $\max\big\{1,\frac{285}{263+385k}\big\}$ for social cost, the latter for $n\ge7$. Finally, we improve several bounds for the real-line pathway model of [Chan and Wang, AAMAS 2023]. Our deterministic maximum-cost lower bound of $2$ matches the upper bound obtainable from [Qin, Fang, and Liu, COCOA 2024]. We strengthen the deterministic social-cost lower bound from $\frac32$ to $2$ under SP and to $\max\{2,n-1\}$ under GSP. For randomized social cost, we sharpen the guarantee of Chan and Wang's proportional mechanism from $6$ to $3$ and raise their lower bound from $1.02$ to $\frac{285}{263}\approx1.08365$ for $n\ge7$.
