{"paper":{"title":"Distance-preserving Subgraphs of Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jaikumar Radhakrishnan, Kshitij Gajjar","submitted_at":"2017-08-10T05:53:02Z","abstract_excerpt":"We consider the problem of finding small distance-preserving subgraphs of undirected, unweighted interval graphs with $k$ terminal vertices.\n  To start with, we show that finding an optimal distance-preserving subgraph is $\\mathsf{NP}$-hard for general graphs. Then, we show that every interval graph admits a subgraph with $O(k)$ branching vertices that approximates pairwise terminal distances up to an additive term of $+1$. We also present an interval graph $G_{\\mathrm{int}}$ for which the $+1$ approximation is necessary to obtain the $O(k)$ upper bound on the number of branching vertices. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03081","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"}