{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QXMEF4BF4XBWNARWFD47UYDIO4","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":"ec012b81e90736421417854c577f52a887b9e6ebaa71a41dee1685030213399d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-29T11:36:01Z","title_canon_sha256":"78ead93bec3d79edd7f0203960313875477212af814ae29f46e33b1be2a66457"},"schema_version":"1.0","source":{"id":"1206.6991","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6991","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6991v3","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6991","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"QXMEF4BF4XBW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QXMEF4BF4XBWNARW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QXMEF4BF","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:de21e31e5aac0e64f7fa7e50a590ec66d4bd661409c231897c9270e143ca7564","target":"graph","created_at":"2026-05-18T03:30:25Z","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":"In this work we consider the mean field traveling salesman problem, where the intercity distances are taken to be i.i.d. with some distribution $F$. This paper focus on the \\emph{nearest neighbor tour} which is to move to the nearest non-visited city and we show that under some conditions on $F$, which are satisfied by exponential distribution with constant mean, the total length of the nearest neighbor tour, asymptotically almost surely scales as $\\log n$. Similar result is known for Euclidean TSP and nearest neighbor tour. We further derive the limiting behavior of the total length of the ne","authors_text":"Antar Bandyopadhyay, Farkhondeh Sajadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-29T11:36:01Z","title":"On the Nearest Neighbor Algorithm for Mean Field Traveling Salesman Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6991","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":"sha256:50396667786c7ccd36ac2719818cf299b33d3c3bc61578a6d5201a158472f6e8","target":"record","created_at":"2026-05-18T03:30:25Z","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":"ec012b81e90736421417854c577f52a887b9e6ebaa71a41dee1685030213399d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-29T11:36:01Z","title_canon_sha256":"78ead93bec3d79edd7f0203960313875477212af814ae29f46e33b1be2a66457"},"schema_version":"1.0","source":{"id":"1206.6991","kind":"arxiv","version":3}},"canonical_sha256":"85d842f025e5c366823628f9fa606877318eed44b6eddc4f527a44ce3c9b2825","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85d842f025e5c366823628f9fa606877318eed44b6eddc4f527a44ce3c9b2825","first_computed_at":"2026-05-18T03:30:25.801964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:25.801964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IUX3sfwvYiIm+40PXysOzbV23ju3oCsjgpEyy62L19jjK9TxfCvMfypQdSaqP6IdunnMddsRorJA8twrSTCvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:25.802628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6991","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50396667786c7ccd36ac2719818cf299b33d3c3bc61578a6d5201a158472f6e8","sha256:de21e31e5aac0e64f7fa7e50a590ec66d4bd661409c231897c9270e143ca7564"],"state_sha256":"3157274b19acaaa72aa8c338c2e9331e482ad94386d3e5a6e59ae3a01457637d"}