Determining the complexity of election attack problems is a major research direction in the computational study of voting problems. The paper "Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters" by Erd\'elyi et al. (JAAMAS 2021) provides a comprehensive study of the complexity of control problems. The sole open problem is constructive control by replacing voters for 2-Approval. We show that this case is in P, strengthening the recent RP (randomized polynomial-time) upper bound due to Fitzsimmons and Hemaspaandra (IJCAI 2022). We show this by transforming 2-Approval CCRV to weighted matching. We also use this approach to show that priced bribery for 2-Veto elections is in P. With this result, and the accompanying (unsurprising) result that priced bribery for 3-Veto elections is NP-complete, this settles the complexity for $k$-Approval and $k$-Veto standard control and bribery cases.

翻译：确定选举攻击问题的复杂度是计算投票问题研究中的一个主要方向。Erdélyi等人（JAAMAS 2021）的论文《迈向完成拼图：通过替换、添加和删除候选人或选民进行控制的复杂度》对控制问题的复杂度进行了全面研究。唯一未解决的问题是关于2-Approval中替换选民的构造性控制。我们证明该问题属于P类，从而强化了Fitzsimmons和Hemaspaandra（IJCAI 2022）近期提出的RP（随机多项式时间）上界。我们通过将2-Approval CCRV转化为加权匹配来证明这一点。我们还利用这一方法证明2-Veto选举中的定价贿赂问题属于P类。结合这一结果以及3-Veto选举中定价贿赂问题为NP完全这一（并不令人意外的）结果，本文确定了$k$-Approval和$k$-Veto标准控制与贿赂问题的复杂度。