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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.4355","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-16T17:43:07Z","cross_cats_sorted":[],"title_canon_sha256":"5fb858c00a81050be20b934ddd56fdc9d548274f71fef92d2188ee854390fd1e","abstract_canon_sha256":"8bbeb3aff9a034cd37b1ab35329a37dfeb6d33235d9d265d23a96f90a93aeef5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:08.434168Z","signature_b64":"DLBwEIpIUcGWCWlW6uI7OQiRxLrGuLQuxjJK2VwfU3oquo1IYeHcM/9Jo6u0MPYr8NS1asPcsYckZBQpw3WuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a463bb18eb3c97428c900c753299d3b78949127a92cadce639985d5c55721dd","last_reissued_at":"2026-05-18T00:13:08.433399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:08.433399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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