{"paper":{"title":"A Short Proof of the VPN Tree Routing Conjecture on Ring Networks","license":"","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Fabrizio Grandoni, Gianpaolo Oriolo, Martin Skutella, Volker Kaibel","submitted_at":"2007-10-16T13:08:15Z","abstract_excerpt":"The VPN Tree Routing Conjecture states that there always exists an optimal solution to the symmetric Virtual Private Network Design (sVPND) problem where the paths between all terminals form a tree. Only recently, Hurkens, Keijsper, and Stougie gave a proof of this conjecture for the special case of ring networks. Their proof is based on a dual pair of linear programs and is somewhat in- volved. We present a short proof of a slightly stronger conjecture which might also turn out to be useful for proving the VPN Tree Routing Conjecture for general networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3044","kind":"arxiv","version":2},"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"}