{"paper":{"title":"Polynomial-Time Approximation Schemes for k-Center and Bounded-Capacity Vehicle Routing in Graphs with Bounded Highway Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amariah Becker, David Saulpic, Philip N. Klein","submitted_at":"2017-07-26T01:43:56Z","abstract_excerpt":"The concept of bounded highway dimension was developed to capture observed properties of the metrics of road networks. We show that a graph with bounded highway dimension, for any vertex, can be embedded into a a graph of bounded treewidth in such a way that the distance between $u$ and $v$ is preserved up to an additive error of $\\epsilon$ times the distance from $u$ or $v$ to the selected vertex. We show that this theorem yields a PTAS for Bounded-Capacity Vehicle Routing in graphs of bounded highway dimension. In this problem, the input specifies a depot and a set of clients, each with a lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08270","kind":"arxiv","version":5},"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"}