{"paper":{"title":"M-convex Function Minimization Under L1-Distance Constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Akiyoshi Shioura","submitted_at":"2018-09-10T04:18:30Z","abstract_excerpt":"In this paper we consider a new problem of minimizing an M-convex function under L1-distance constraint (MML1); the constraint is given by an upper bound for L1-distance between a feasible solution and a given \"center.\" This is motivated by a nonlinear integer programming problem for re-allocation of dock capacity in a bike sharing system discussed by Freund et al. (2017). The main aim of this paper is to better understand the combinatorial structure of the dock re-allocation problem through the connection with M-convexity, and show its polynomial-time solvability using this connection. For th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03126","kind":"arxiv","version":3},"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"}