{"paper":{"title":"Faster Exponential-Time Approximate Counting via Bounded Self-Reductions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Katie Clinch, Qi Wang, Serge Gaspers, Simon Mackenzie","submitted_at":"2026-07-07T15:25:53Z","abstract_excerpt":"We give faster exponential-time randomised approximation algorithms for counting problems where polynomial-time approximation is unavailable and exact exponential-time counting remains expensive. For general \\(n\\)-vertex graphs, our independent-set counter runs in \\(O^{\\ast}(1.1869^{n})\\) time, improving the previous \\(O^{\\ast}(1.2041^{n})\\) general-graph bound. For \\(n\\)-variable \\#\\textsc{2-SAT}, we obtain an \\(O^{\\ast}(1.2373^{n})\\)-time approximation algorithm, narrowly below Wahlstr{\\\"o}m's currently cited \\(O^{\\ast}(1.2377^{n})\\) variable-parameter exact bound.\n  The new algorithmic poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06393","kind":"arxiv","version":1},"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/2607.06393/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"}