{"paper":{"title":"Approximation Complexity of Max-Cut on Power Law Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO","math.OC"],"primary_cat":"cs.DS","authors_text":"Marek Karpinski, Mathias Hauptmann, Mikael Gast","submitted_at":"2016-02-26T15:32:29Z","abstract_excerpt":"In this paper we study the MAX-CUT problem on power law graphs (PLGs) with power law exponent $\\beta$. We prove some new approximability results on that problem. In particular we show that there exist polynomial time approximation schemes (PTAS) for MAX-CUT on PLGs for the power law exponent $\\beta$ in the interval $(0,2)$. For $\\beta>2$ we show that for some $\\epsilon>0$, MAX-CUT is NP-hard to approximate within approximation ratio $1+\\epsilon$, ruling out the existence of a PTAS in this case. Moreover we give an approximation algorithm with improved constant approximation ratio for the case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08369","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"}