{"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 $v\\not\\in S$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.04278","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.04278/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}