{"paper":{"title":"Long-term planning versus short-term planning in the asymptotical location problem","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"A. Brancolini, E. Stepanov, F. Santambrogio, G. Buttazzo","submitted_at":"2006-12-22T18:36:52Z","abstract_excerpt":"Given the probability measure $\\nu$ over the given region $\\Omega\\subset \\R^n$, we consider the optimal location of a set $\\Sigma$ composed by $n$ points $\\Om$ in order to minimize the average distance $\\Sigma\\mapsto \\int_\\Om \\dist(x,\\Sigma) d\\nu$ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the configuration bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612718","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"}