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Here, we give the first subexponential parameterized algorithm solving Minimum Fill-in in time O(2^(O(\\sqrt{k} log k)) + k2 * nm). This substantially lower the complexity of the problem. Techniques developed for Minimum Fill-in can be used to obtain subexponential parameterized algorithms for several related probl"},"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":"1104.2230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-12T14:39:13Z","cross_cats_sorted":[],"title_canon_sha256":"a0bb83debb047d8d965d2d9b278bb3aca379f3d1d4986cc94206b0eac57f5935","abstract_canon_sha256":"0b50711685fc43ccc25ba50b7a5552218fb4f11bb554254d62c7b63023123749"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:35.704617Z","signature_b64":"RTozbD1vz3eFdiXbXm8LHxKZ4/MVVCS3D0RfCYSX/JULLtYo9gu3DnlRnM4++giRDIfYBaMTieS36CcfVsyZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bb89bc854702b834f42ed91b4aa18d7c7106ddd1eef732e5b6f8cba9193b666","last_reissued_at":"2026-05-18T04:24:35.704122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:35.704122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subexponential Parameterized Algorithm for Minimum Fill-in","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fedor V. 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