{"paper":{"title":"Hardness, Approximability, and Fixed-Parameter Tractability of the Clustered Shortest-Path Tree Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.NI"],"primary_cat":"cs.DS","authors_text":"Daniele Frigioni, Guido Proietti, Luca Forlizzi, Mattia D'Emidio, Stefano Leucci","submitted_at":"2018-01-31T12:02:04Z","abstract_excerpt":"Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \\emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$, subject to some additional constraint on its clusters.\n  In particular, we focus on the classic problem of designing a \\emph{single-source shortest-path tree}, and we analyze its computational hardness when in a feasible solution each cluster is required to form a subtree. We first study the \\emph{unweighted} case, and prove that the problem is \\np-hard. How"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10416","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"}