{"paper":{"title":"Constructing Optimal Highways","license":"","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexander Wolff, Chan-Su Shin, Christian Knauer, Hee-Kap Ahn, Helmut Alt, Hyeon-Suk Na, Otfried Cheong, Peter Brass, Sang Won Bae, Tetsuo Asano","submitted_at":"2007-03-08T17:22:21Z","abstract_excerpt":"For two points $p$ and $q$ in the plane, a straight line $h$, called a highway, and a real $v>1$, we define the \\emph{travel time} (also known as the \\emph{city distance}) from $p$ and $q$ to be the time needed to traverse a quickest path from $p$ to $q$, where the distance is measured with speed $v$ on $h$ and with speed 1 in the underlying metric elsewhere.\n  Given a set $S$ of $n$ points in the plane and a highway speed $v$, we consider the problem of finding a \\emph{highway} that minimizes the maximum travel time over all pairs of points in $S$. If the orientation of the highway is fixed, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0703037","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"}