{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PECWWGAIP6TED55D6CWKWAS52G","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":"c1bf09c75ff006400120246715b84e687773673d52fb89b50bff09ff2568661a","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-13T07:01:48Z","title_canon_sha256":"58d07dadad90f609c978453911d44733f4a719000f5a196a79b86e1bc7966534"},"schema_version":"1.0","source":{"id":"1707.03992","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03992","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03992v4","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03992","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"PECWWGAIP6TE","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PECWWGAIP6TED55D","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PECWWGAI","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:4bc692e2cc936115a761dcad82f53ba2da76d5452451025293f260f08893b89c","target":"graph","created_at":"2026-05-17T23:39:58Z","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":"We show that there is a polynomial-time algorithm with approximation guarantee $\\frac{3}{2}+\\epsilon$ for the $s$-$t$-path TSP, for any fixed $\\epsilon>0$. It is well known that Wolsey's analysis of Christofides' algorithm also works for the $s$-$t$-path TSP with its natural LP relaxation except for the narrow cuts (in which the LP solution has value less than two). A fixed optimum tour has either a single edge in a narrow cut (then call the edge and the cut lonely) or at least three (then call the cut busy). Our algorithm \"guesses\" (by dynamic programming) lonely cuts and edges. Then we parti","authors_text":"Jens Vygen, Vera Traub","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-13T07:01:48Z","title":"Approaching $\\frac{3}{2}$ for the $s$-$t$-path TSP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03992","kind":"arxiv","version":4},"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":"sha256:018d7f951105de40a1bf574b528cb101a8479eb287cd3802722e79e86125dcd6","target":"record","created_at":"2026-05-17T23:39:58Z","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":"c1bf09c75ff006400120246715b84e687773673d52fb89b50bff09ff2568661a","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-13T07:01:48Z","title_canon_sha256":"58d07dadad90f609c978453911d44733f4a719000f5a196a79b86e1bc7966534"},"schema_version":"1.0","source":{"id":"1707.03992","kind":"arxiv","version":4}},"canonical_sha256":"79056b18087fa641f7a3f0acab025dd1b74197aad2ed9c2e6d489ea2d1acf8bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79056b18087fa641f7a3f0acab025dd1b74197aad2ed9c2e6d489ea2d1acf8bd","first_computed_at":"2026-05-17T23:39:58.924034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:58.924034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"unf3gA2PZ6JJ4IFKvYAwPDF1UmD5gafNd5WS4VWRBKqiL81r8JXLK5WuoPbH6pN8dLV8iWd6Y6X3rj+Gn840Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:58.924650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03992","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:018d7f951105de40a1bf574b528cb101a8479eb287cd3802722e79e86125dcd6","sha256:4bc692e2cc936115a761dcad82f53ba2da76d5452451025293f260f08893b89c"],"state_sha256":"b7cf82cc5d6ebaeb8f918cebef650bde00ead8601c0df7d35aec85a1d0d3e12a"}