Problem
Research questions and friction points this paper is trying to address.
truthful interval covering
unit interval
approximation ratio
strategyproof lottery
order-statistic mechanisms
Optimal Rank Lotteries for Truthful Unit-Interval Covering
🤖 AI Summary
本文解决了真实单位区间覆盖问题，通过优化秩彩票机制，以最小化未覆盖长度并激励代理说实话，达到了3/2的近似比。
📝 Abstract
In truthful interval covering, each agent has a private interval of unit length, and the goal is to decide where to place a public unit interval so as to minimize the total uncovered length while incentivizing the agents to be truthful. Previous work proposed a universally strategyproof lottery over order-statistic mechanisms with approximation ratio at most $5/3$, and established a lower bound of $3/2-o(1)$ for this class of mechanisms. We close this gap by characterizing the approximation ratio of every report-independent lottery over order-statistics. In particular, we show that, for every $n\ge2$, the optimal approximation ratio for this class is $\frac32-\frac{1}{2\lfloor n/2\rfloor}$. Beyond rank lotteries, we show that every universally strategyproof randomized mechanism has approximation ratio at least $9/8$.
Innovation
Methods, ideas, or system contributions that make the work stand out.
universally strategyproof
approximation ratio
order-statistic mechanisms
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2023-03-14International Symposium on Computational GeometryCitations: 5
