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Vistisen, Sampson Wong, Sarita de Berg","cross_cats":["cs.DS"],"headline":"Persistent data structures maintain a (1+ε)-spanner for dynamic disk intersection graphs with bounded diameters.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-04-28T09:07:25Z","title":"A dynamic $(1+\\varepsilon)$-spanner for disk intersection graphs"},"references":{"count":17,"internal_anchors":0,"resolved_work":17,"sample":[{"cited_arxiv_id":"","doi":"10.4230/lipics.socg.2015.186","is_internal_anchor":false,"ref_index":1,"title":"Geometric spanners for points inside a polygonal domain","work_id":"0ededbb4-271e-423c-9d04-3ff5162f4961","year":2015},{"cited_arxiv_id":"","doi":"10.1109/sfcs.1998.743504","is_internal_anchor":false,"ref_index":2,"title":"4 Ingo Althöfer, Gautam Das, David P","work_id":"761aec79-405c-4087-82b5-4f9db1202504","year":1998},{"cited_arxiv_id":"","doi":"10.1007/bf02189308","is_internal_anchor":false,"ref_index":3,"title":"5 Shinwoo An, Eunjin Oh, and Jie Xue","work_id":"a59d4e23-f6fc-4acd-9015-9584ea95565e","year":2025},{"cited_arxiv_id":"","doi":"10.1137/19m1246493","is_internal_anchor":false,"ref_index":4,"title":"34 A dynamic(1 +ε)-spanner for disk intersection graphs 21 Timothy M","work_id":"2aa90d24-5a25-4e4e-bea4-75e42b3ffacb","year":null},{"cited_arxiv_id":"","doi":"10.4230/lipics.socg.2023.23","is_internal_anchor":false,"ref_index":5,"title":"doi:10.4230/LIPIcs.SoCG.2023.23","work_id":"d4148f61-83b1-470d-98b3-989791f3c829","year":2023}],"snapshot_sha256":"8ad569cbdf07861b71cad2fc81e87c588c79e8c3b5c08d53088e303d0da2e547"},"source":{"id":"2604.25397","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-07T13:48:27.312915Z","id":"e059a77a-5dc2-421b-95ee-b9d06aca6d18","model_set":{"reader":"grok-4.3"},"one_line_summary":"A dynamic (1+ε)-spanner of size O(n ε^{-2} log Ψ log(ε^{-1})) with O((Ψ/ε)^2 log^4 n log^2 Ψ log^2(ε^{-1})) expected amortized update time for disk intersection graphs with bounded diameters.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Persistent data structures maintain a (1+ε)-spanner for dynamic disk intersection graphs with bounded diameters.","strongest_claim":"We maintain a (1+ε)-spanner over the disk intersection graph of a dynamic set of disks with diameters in [4, Ψ]. The spanner has size O(n ε^{-2} log Ψ log(ε^{-1})), uses O(ε^{-2} n log^4 n log Ψ) space, and supports updates in O((Ψ/ε)^2 log^4 n log^2 Ψ log^2(ε^{-1})) expected amortized time. For constant ε and Ψ the bounds become near-linear size, near-linear space, and polylogarithmic updates. The same spanner supports connectivity queries.","weakest_assumption":"All disks have diameters restricted to the fixed known interval [4, Ψ]; without this bounded-diameter assumption the size and update bounds no longer hold and the persistent-structure approach may not apply directly."}},"verdict_id":"e059a77a-5dc2-421b-95ee-b9d06aca6d18"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6fc8856572b1968bae66d705dfcaac55334a3fecb7b070bfe6a6ac278005c31b","target":"record","created_at":"2026-05-20T00:00:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"443f7d519b2f2ae5343e757fd1c45ee26c253a54a4c7631ef644a95efa52f1f3","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-04-28T09:07:25Z","title_canon_sha256":"f5df67445dee46faef61c3c755fba7e8b52f71261903e5d8a076c96b6148a4fe"},"schema_version":"1.0","source":{"id":"2604.25397","kind":"arxiv","version":1}},"canonical_sha256":"1513530970632468e4c2ff8cf5514335aabce3ce302d0ac1dc572f12cfb4001e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1513530970632468e4c2ff8cf5514335aabce3ce302d0ac1dc572f12cfb4001e","first_computed_at":"2026-05-20T00:00:39.478666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:39.478666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNbI7DLGm393Qw3Zi59jVxWDKNramCkKKfZ0vf5vBzHgBQGYwBV5lC8WrZhqndgn5dAaDgav6ojE+e+uzp5zCw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:39.479418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.25397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:709739aec17f209d7707d5dd21d0eed0a41105cce1008f2faf8b6284f0b0e28c","sha256:6fc8856572b1968bae66d705dfcaac55334a3fecb7b070bfe6a6ac278005c31b","sha256:8098620180d440a824aa77483948e04f22eb07911781d3b83c471467966c6f8a"],"state_sha256":"39093fac8df4e71c19baa4ae1ace37ccf17775d96fc4fde087046e14a691cea8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1s1kmFlg/uYe5IctOgAsV7aV7XAKMXEqVYZ7ysi0TghCx9KJMxaBDBoO39CfFa9b/eYUPEqCK9rAuOH4LD7BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T11:13:01.703689Z","bundle_sha256":"ca378f411c2e92d11cf921ab145fd6d1fbc10d14eff2243303fad3c8a847e47e"}}