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We show that our algorithms run in time $O^{*}(t(P))$ and $O^{*}(pt(P))$ respectively, where $t(P)$ and $pt(P)$ are the largest number of triangulation paths (T-paths) and pseudo-triangulations paths (PT-paths), respectively, that the algorithms encounter during their execution. Moreover, we show that $t(P) = O^{*}(9^{n})$, which is the first non-trivial bound on $t(P)$ to be known.\n  Wh"},"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":"1312.3188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-11T14:34:12Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"e50b6b88a61ce3aa244a896993f875b72e71bb6669eaa8206647dba778111eac","abstract_canon_sha256":"0bbf292584ed1c59760bc8030795f05adc3d3ac4b4839e58b2a70da89bc1b0fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:00.255905Z","signature_b64":"2RhwJB3T+beNsQdL+TTDCAR6p+sP4qvXzsAfBIhpljf4IOomnJ+o8czi+Y4zbiup/28YvbaPJRxe7WzER3VpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"318b74cabbd9e7441bfe0fc1fc59264b6e987a0c6e0cbc85b34e45ac5145a485","last_reissued_at":"2026-05-18T03:05:00.255427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:00.255427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Simple Sweep Line Algorithm for Counting Triangulations and Pseudo-triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.CG","authors_text":"Karl Bringmann, Saurabh Ray, Victor Alvarez","submitted_at":"2013-12-11T14:34:12Z","abstract_excerpt":"Let $P\\subset\\mathbb{R}^{2}$ be a set of $n$ points. 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