{"paper":{"title":"Hardness Results for Consensus-Halving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.GT","authors_text":"Aris Filos-Ratsikas, Jie Zhang, Paul W. Goldberg, Soren Kristoffer Stiil Frederiksen","submitted_at":"2016-09-16T16:51:23Z","abstract_excerpt":"We study the consensus-halving problem of dividing an object into two portions, such that each of $n$ agents has equal valuation for the two portions. The $\\epsilon$-approximate consensus-halving problem allows each agent to have an $\\epsilon$ discrepancy on the values of the portions. We prove that computing $\\epsilon$-approximate consensus-halving solution using $n$ cuts is in PPA, and is PPAD-hard, where $\\epsilon$ is some positive constant; the problem remains PPAD-hard when we allow a constant number of additional cuts. It is NP-hard to decide whether a solution with $n-1$ cuts exists for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05136","kind":"arxiv","version":2},"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"}