{"paper":{"title":"New Tools and Connections for Exponential-time Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Bundit Laekhanukit, Danupon Nanongkai, Jesper Nederlof, Nikhil Bansal, Parinya Chalermsook","submitted_at":"2017-08-11T12:16:47Z","abstract_excerpt":"In this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and a parameter $\\alpha>1$, and the goal is to design an $\\alpha$-approximation algorithm with the fastest possible running time. We show the following results:\n  - An $r$-approximation for maximum independent set in $O^*(\\exp(\\tilde O(n/r \\log^2 r+r\\log^2r)))$ time,\n  - An $r$-approximation for chromatic number in $O^*(\\exp(\\tilde{O}(n/r \\log r+r\\log^2r)))$ time,\n  - A $(2-1/r)$-approximation for minimum vertex cover in $O^*(\\exp(n/r^{\\Omega(r)}))$ time, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03515","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"}