{"paper":{"title":"Sublinear Approximation Algorithms for Boxicity and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Abhijin Adiga, Jasine Babu, L. Sunil Chandran","submitted_at":"2015-05-19T09:19:39Z","abstract_excerpt":"Boxicity of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes in $\\mathbb{R}^k$. Cubicity is a variant of boxicity, where the axis parallel boxes in the intersection representation are restricted to be of unit length sides. Deciding whether boxicity (resp. cubicity) of a graph is at most k is NP-hard, even for k=2 or 3. Computing these parameters is inapproximable within $O(n^{1 - \\epsilon})$-factor, for any $\\epsilon >0$ in polynomial time unless NP=ZPP, even for many simple graph classes.\n  In this paper, we give a polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04918","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"}