{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2LVBYMLEDULEGBPMMUB3WH6RI7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"71c6c686433b98c1f51c942d198c339295d10bb4e7c84dbe3a354dcedea1eb59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-20T20:05:48Z","title_canon_sha256":"b12bc4fcf77781c60584bb662bef29d9a993970a6871316546b6bb8cb27d5bd9"},"schema_version":"1.0","source":{"id":"1311.5197","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5197","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5197v3","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5197","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"pith_short_12","alias_value":"2LVBYMLEDULE","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2LVBYMLEDULEGBPM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2LVBYMLE","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:b6ab2c5c555fdade2fa48e42e9d500ca00388521d06f8e8c6345ac51b802c40a","target":"graph","created_at":"2026-05-18T01:34:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A bottleneck plane perfect matching of a set of $n$ points in $\\mathbb{R}^2$ is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as {\\em bottleneck}. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck plane matching of size at least $\\frac{n}{5}$ in $O(n \\log^2 n)$-time. Then we extend our idea toward an $O(n\\log n)$-time approximation algorithm which computes a plane matching of size at least $\\frac{2n}{5}$ whose edges","authors_text":"Ahmad Biniaz, A. Karim Abu-Affash, Anil Maheshwari, Michiel Smid, Paz Carmi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-20T20:05:48Z","title":"Approximating the Bottleneck Plane Perfect Matching of a Point Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5197","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:67481740952a724f7a72a631b6294ed16b3ba24ed4d0438a3da90dcb56ad96b9","target":"record","created_at":"2026-05-18T01:34:55Z","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":"71c6c686433b98c1f51c942d198c339295d10bb4e7c84dbe3a354dcedea1eb59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-20T20:05:48Z","title_canon_sha256":"b12bc4fcf77781c60584bb662bef29d9a993970a6871316546b6bb8cb27d5bd9"},"schema_version":"1.0","source":{"id":"1311.5197","kind":"arxiv","version":3}},"canonical_sha256":"d2ea1c31641d164305ec6503bb1fd147d6b54ceb2d10e2b424ac415c94759f97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2ea1c31641d164305ec6503bb1fd147d6b54ceb2d10e2b424ac415c94759f97","first_computed_at":"2026-05-18T01:34:55.673281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:55.673281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zRwn/gNXj2YtH8PNH3fD3fVRQm7wQ8OddWW2PQ0Wh2zqRjuP5b6Zoyvba8nhPQ58amoWr+4nGmlhA+J7k0TEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:55.673915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5197","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67481740952a724f7a72a631b6294ed16b3ba24ed4d0438a3da90dcb56ad96b9","sha256:b6ab2c5c555fdade2fa48e42e9d500ca00388521d06f8e8c6345ac51b802c40a"],"state_sha256":"a27deef47220cc4c78f9e78e45a550b560f72a3798e34ed4b5b53950785b600f"}