{"paper":{"title":"Near Linear Time Approximation Schemes for Uncapacitated and Capacitated b--Matching Problems in Nonbipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kook Jin Ahn, Sudipto Guha","submitted_at":"2013-07-16T17:43:07Z","abstract_excerpt":"We present the first near optimal approximation schemes for the\n  maximum weighted (uncapacitated or capacitated) $b$--matching\n  problems for non-bipartite graphs that run in time (near) linear in\n  the number of edges. For any $\\delta>3/\\sqrt{n}$ the algorithm\n  produces a $(1-\\delta)$ approximation in $O(m \\poly(\\delta^{-1},\\log\n  n))$ time. We provide fractional solutions for the standard linear\n  programming formulations for these problems and subsequently also\n  provide (near) linear time approximation schemes\n  for rounding the fractional solutions.\n  Through these problems as a vehicle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4355","kind":"arxiv","version":4},"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"}