{"paper":{"title":"The Control Complexity of $r$-Approval: from the Single-Peaked Case to the General Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Jiong Guo, Yongjie Yang","submitted_at":"2013-04-16T14:41:44Z","abstract_excerpt":"We investigate the complexity of $r$-Approval control problems in $k$-peaked elections, where at most $k$ peaks are allowed in each vote with respect to an order of the candidates. We show that most NP-hardness results in general elections also hold in k-peaked elections even for $k=2,3$. On the other hand, we derive polynomial-time algorithms for some problems for $k=2$. All our NP-hardness results apply to Approval and sincere-strategy preference-based Approval as well. Our study leads to many dichotomy results for the problems considered in this paper, with respect to the values of $k$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4471","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}