{"paper":{"title":"Approximation of barter exchanges with cycle length constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Chenggang Wu, Jianyang Zeng, Pingzhong Tang, Suiqian Luo","submitted_at":"2016-05-28T09:00:20Z","abstract_excerpt":"We explore the clearing problem in the barter exchange market. The problem, described in the terminology of graph theory, is to find a set of vertex-disjoint, length-restricted cycles that maximize the total weight in a weighted digraph. The problem has previously been shown to be NP-hard. We advance the understanding of this problem by the following contributions.\n  We prove three constant inapproximability results for this problem. For the weighted graphs, we prove that it is NP-hard to approximate the clearing problem within a factor of 14/13 under general length constraints and within a fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08863","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"}