arXiv subjects

Jianan Lin

Publications and source records attributed to Jianan Lin.

3 recordsLinked to original sources

arXiv2026

Strategyproof Mechanisms for Connecting Impassable Regions

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 $n\ge7$.

cs.GT↗

arXiv2026

Improved Randomized Approximations for Strategic Obnoxious Facility Location

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.

cs.GT↗

arXiv2026

Randomized Strategyproof Facility Location: Two Facilities and Beyond

We design and analyze randomized strategyproof mechanisms for multi-facility location under the utilitarian social-cost objective, the sum of the agents' distances to their nearest facilities. For two facilities, the Pairwise-Distance mechanism locates facilities at a pair of reported locations sampled with probability proportional to their distance. It is strategyproof on Ptolemaic spaces, including Euclidean and Hilbert spaces as special cases, and has an approximation ratio of $4$. The resulting Hybrid-Distance mechanism is a fixed-probability mixture: it selects the classical Proportional mechanism [Lu et al., EC'10] with probability $λ^*=\frac{5+4\sqrt3}{23}$ and Pairwise-Distance with probability $1-λ^*$. It is strategyproof on Ptolemaic spaces and has a tight approximation ratio of $\frac{74+4\sqrt3}{23}\approx3.5186$, breaking the long-standing factor-$4$ benchmark of [Lu et al., EC'10]. We complement the two-facility results by studying more facilities. First, for $n$ agents and $k=n-1$ facilities, we introduce the Inverse-Square mechanism, which omits one report with probability proportional to the inverse square of its nearest-neighbor distance and locates facilities at all remaining reports. It is strategyproof on any metric space and has an approximation ratio of $Θ(\sqrt{n})$, improving the previous best-known ratio of $\frac{n}{2}$ [Escoffier et al., ADT'11]. Second, for $k$ facilities on the line, we introduce the Gap-Product mechanism, which locates facilities at $k$ reports and weights each set by the product of the gaps between consecutive selected reports. When $k=3$, it is strategyproof and has a $6$-approximation, replacing the previous $n$-dependent guarantee [Fotakis and Tzamos, EC'13] by a constant, whereas it is not strategyproof for any $k\ge4$.

cs.GT↗