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The problem of finding a $(\\sigma,\\rho)$-set (of a certain size) unifies standard problems such as Independent Set, Dominating Set, Independent Dominating Set, and many others.\n  For all pairs of finite or cofinite sets $(\\sigma,\\rho)$, we determine (under st"},"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":"2211.04278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-11-08T14:36:12Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2a939c8f08fb8cc60a609ed775c25919c231b83c74330bd9e4fef1956de56b91","abstract_canon_sha256":"0e340d65d6892505b3bc493768ea7d5f34357bce8e333c0f57e75b47e2f659e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:03.044670Z","signature_b64":"KH8A38RU4ipvfwuSRoxiaFiM/1CZQxjimiL50wVYSgM0dpvSDAn06TmJ6RSaizAeRtYzfkRX5dWP1YYqpaWsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f365a86162741e18f6d3e57a17072ec3e7363cf43efcc1f2fdd514316f13d7d6","last_reissued_at":"2026-07-05T10:51:03.044153Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:03.044153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs Part I: Algorithmic Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"D\\'aniel Marx, Daniel Neuen, Fionn Mc Inerney, Govind S. Sankar, Jacob Focke, Philipp Schepper, Philip Wellnitz","submitted_at":"2022-11-08T14:36:12Z","abstract_excerpt":"We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\\sigma,\\rho$ of non-negative integers, a $(\\sigma,\\rho)$-set of a graph $G$ is a set $S$ of vertices such that $|N(u)\\cap S|\\in \\sigma$ for every $u\\in S$, and $|N(v)\\cap S|\\in \\rho$ for every $v\\not\\in S$. 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