AI 中文总结
研究参与式预算选举中候选人控制问题，聚焦GreedyAV和GreedyCost规则，因其NP难，从参数化复杂性和近似性角度分析，对相关自然参数及组合全面分类并建立近似性边界。
AI 中文摘要
我们研究参与式预算选举中的候选人控制问题。重点关注两种著名的基于顺序福利的规则——GreedyAV和GreedyCost，它们在实践中广泛使用。候选人控制问题是能否策略性地修改可用候选人集合，以确保首选候选人p被选中或阻止p被选中。由于这两种规则下的所有候选人控制变体都是NP难的，我们从参数化复杂性和近似性角度分析问题。一方面，针对选民数量、受控候选人数量等自然参数及其组合给出全面分类；另一方面，建立了紧密的近似性边界。
英文摘要
We study the problem of candidate control in participatory budgeting elections. Our focus is on two prominent sequential welfare-based rules---GreedyAV and GreedyCost---which are widely used in practice. Candidate control asks whether we can strategically modify the set of available candidates so as to either ensure that a preferred candidate $p$ is selected or prevent $p$ from being selected. Since all variants of candidate control under the two rules we consider are known to be NP-hard, we analyze the problems through the lens of parameterized complexity and approximability. Under the first lens, we provide a comprehensive classification with respect to natural parameters such as the number of voters, the number of controlled candidates, and the number of distinct costs, as well as their combinations. Within the second perspective, we establish a tight approximability bound.
