{"paper":{"title":"Hardness of the Pricing Problem for Chains in Barter Exchanges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.DS","authors_text":"Benjamin Plaut, John P. Dickerson, Tuomas Sandholm","submitted_at":"2016-06-01T04:49:08Z","abstract_excerpt":"Kidney exchange is a barter market where patients trade willing but medically incompatible donors. These trades occur via cycles, where each patient-donor pair both gives and receives a kidney, and via chains, which begin with an altruistic donor who does not require a kidney in return. For logistical reasons, the maximum length of a cycle is typically limited to a small constant, while chains can be much longer. Given a compatibility graph of patient-donor pairs, altruists, and feasible potential transplants between them, finding even a maximum-cardinality set of vertex-disjoint cycles and ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00117","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"}