{"paper":{"title":"Paths and Intersections: Recognizing Outerplanar Metrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Yu Chen, Zihan Tan","submitted_at":"2026-06-24T13:45:01Z","abstract_excerpt":"We study the following distance realization problem: given a metric $D$ on a set $T$ of terminals, does there exist an (edge-weighted) outerplanar graph $G$, such that $T\\subseteq V(G)$, and for every pair $t,t'\\in T$, $\\textsf{dist}_G(t,t')=D(t,t')$? We first prove that there is no ``local characterization'', forming a contrast with trees and Okamura-Seymour instances. Our main result is an efficient algorithm for this problem whose running time is polynomial in $|T|$.\n  Both our proof and our algorithm utilize a recent new approach of analyzing graph structures, by viewing graphs as paths an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25827","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25827/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}