{"paper":{"title":"Exact Algorithms for Weighted and Unweighted Borda Manipulation Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.DS","authors_text":"Jiong Guo, Yongjie Yang","submitted_at":"2013-04-10T21:05:08Z","abstract_excerpt":"Both weighted and unweighted Borda manipulation problems have been proved $\\mathcal{NP}$-hard. However, there is no exact combinatorial algorithm known for these problems. In this paper, we initiate the study of exact combinatorial algorithms for both weighted and unweighted Borda manipulation problems. More precisely, we propose $O^*((m\\cdot 2^m)^{t+1})$time and $O^*(t^{2m})$time\\footnote{$O^*()$ is the $O()$ notation with suppressed factors polynomial in the size of the input.} combinatorial algorithms for weighted and unweighted Borda manipulation problems, respectively, where $t$ is the nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3145","kind":"arxiv","version":1},"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"}