{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GUK6W2VFPO2FO2YOBIKNDBBBYY","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":"e38beaeda68c9047cc9f2c240bb1445cad3cd9878e81847361ce7dc7d3b2bced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-21T10:05:22Z","title_canon_sha256":"8deacae76aead62a3fdee7eb30c9b40e4b35b9e2e9dd986afa88c7030578f63f"},"schema_version":"1.0","source":{"id":"1412.6755","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6755","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6755v1","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6755","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"pith_short_12","alias_value":"GUK6W2VFPO2F","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GUK6W2VFPO2FO2YO","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GUK6W2VF","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:c83540ad7c263a727dc9be51bd09e1de6c1e95e2e9426bb0c61561eeda0ffbe8","target":"graph","created_at":"2026-05-18T02:30:46Z","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":"Given a complete edge-weighted graph G, we present a polynomial time algorithm to compute a degree-four-bounded spanning Eulerian subgraph of 2G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm and a novel use of orientations in graphs, we obtain a (3 beta/4 + 3 beta^2/4)-approximation algorithm for TSP with beta-relaxed triangle inequality (beta-TSP), where beta >= 1. A graph G is an instance of beta-TSP, if it is a complete graph with non-negative edge weights that are restricted as follows. For each triple of vertices u,v,w in V(G), c({u,v}) <= ","authors_text":"Tobias M\\\"omke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-21T10:05:22Z","title":"An Improved Approximation Algorithm for the Traveling Salesman Problem with Relaxed Triangle Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6755","kind":"arxiv","version":1},"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":"sha256:038c86d45cec93bb04d857b5a2b338416649a0d790a49f7204ae306439e16ac9","target":"record","created_at":"2026-05-18T02:30:46Z","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":"e38beaeda68c9047cc9f2c240bb1445cad3cd9878e81847361ce7dc7d3b2bced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-21T10:05:22Z","title_canon_sha256":"8deacae76aead62a3fdee7eb30c9b40e4b35b9e2e9dd986afa88c7030578f63f"},"schema_version":"1.0","source":{"id":"1412.6755","kind":"arxiv","version":1}},"canonical_sha256":"3515eb6aa57bb4576b0e0a14d18421c603941df74cd5a4e8edd85a804df6d2dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3515eb6aa57bb4576b0e0a14d18421c603941df74cd5a4e8edd85a804df6d2dc","first_computed_at":"2026-05-18T02:30:46.293307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:46.293307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ueB+NqtB2PfcTk+WqwemJUi6ExjOa+I7Ee6EbwyV/Tsvszbx0xmUSy3NO6KsgGvKyt6/JuJVINllGYBTT1aEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:46.293711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6755","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:038c86d45cec93bb04d857b5a2b338416649a0d790a49f7204ae306439e16ac9","sha256:c83540ad7c263a727dc9be51bd09e1de6c1e95e2e9426bb0c61561eeda0ffbe8"],"state_sha256":"5b54f5578fd5addc0fe52c1483096acb2557360fb50609082ad573c70901c68b"}