{"paper":{"title":"Parameterized Algorithms for Zero Extension and Metric Labelling Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Felix Reidl, Magnus Wahlstr\\\"om","submitted_at":"2018-02-16T16:53:44Z","abstract_excerpt":"We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from parameterized complexity.\n  Depending on the chosen cost function $\\mu$, we find that different algorithmic approaches can be applied to design FPT-algorithms: for arbitrary $\\mu$ we parameterized by the number of edges that cross the cut (not the cost) and show how to solve ZERO EXTENSION in time $O(|D|^{O(k^2)} n^4 \\log n)$ using randomized contractions. We improv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06026","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"}