{"paper":{"title":"Incremental Network Design with Minimum Spanning Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.CO","authors_text":"Konrad Engel, Martin W.P. Savelsbergh, Thomas Kalinowski","submitted_at":"2013-06-08T14:49:22Z","abstract_excerpt":"Given an edge-weighted graph $G=(V,E)$ and a set $E_0\\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\\ldots,e'_T\\in E\\setminus E_0$ minimizing $\\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\\cup\\{e'_1,\\ldots,e'_t\\})$ and $T=\\lvert E\\setminus E_0\\rvert$. We prove that this problem can be solved by a greedy algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1926","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"}