{"paper":{"title":"The optimal assignment problem for a countable state space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Marianne Akian, Stephane Gaubert, Vassili Kolokoltsov","submitted_at":"2008-12-30T09:43:59Z","abstract_excerpt":"Given a square matrix B=(b_{ij}) with real entries, the optimal assignment problem is to find a bijection s between the rows and the columns maximising the sum of the b_{is(i)}. In discrete optimal control and in the theory of discrete event systems, one often encounters the problem of solving the equation Bf=g for a given vector g, where the same symbol B denotes the corresponding max-plus linear operator, (Bf)_i:=max_j (b_{ij}+f_j). The matrix B is said to be strongly regular when there exists a vector g such that the equation Bf=g has a unique solution f. A result of Butkovic and Hevery sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4866","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"}