{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:J4ASZ3ZKMP3NHIB5KIB326QKFK","short_pith_number":"pith:J4ASZ3ZK","schema_version":"1.0","canonical_sha256":"4f012cef2a63f6d3a03d5203bd7a0a2a82dd75928796b051e0948b579661e7db","source":{"kind":"arxiv","id":"1703.05559","version":2},"attestation_state":"computed","paper":{"title":"Improving TSP tours using dynamic programming over tree decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arkadiusz Socala, Lukasz Kowalik, Marek Cygan","submitted_at":"2017-03-16T11:09:25Z","abstract_excerpt":"Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local optimum by starting from an arbitrary tour $H$ and then improving it by a sequence of $k$-moves.\n  Until 2016, the only known algorithm to find an improving $k$-move for a given tour was the naive solution in time $O(n^k)$. At ICALP'16 de Berg, Buchin, Jansen and Woeginger showed an $O(n^{\\lfloor 2/3k \\rfloor+1})$-time algorithm.\n  We show an algorithm which r"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.05559","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-16T11:09:25Z","cross_cats_sorted":[],"title_canon_sha256":"4af6ae193a8b8cd34bee6b02a58e0d62c8d3e84dcaaa5136772227fe65a37fc1","abstract_canon_sha256":"cb0989038bb185c81a1691631db5148dbf7c4439073d04e0c9a270abaac35ae3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:06.715414Z","signature_b64":"CNCmdoB5GhPDvrYXP5vwFVYnbBESW/7wAHpd6i/9qzZwPBBMlzTywW6kPm/J5lx3GVDergnHPzYotJrLwBfaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f012cef2a63f6d3a03d5203bd7a0a2a82dd75928796b051e0948b579661e7db","last_reissued_at":"2026-05-18T00:39:06.714792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:06.714792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improving TSP tours using dynamic programming over tree decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arkadiusz Socala, Lukasz Kowalik, Marek Cygan","submitted_at":"2017-03-16T11:09:25Z","abstract_excerpt":"Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local optimum by starting from an arbitrary tour $H$ and then improving it by a sequence of $k$-moves.\n  Until 2016, the only known algorithm to find an improving $k$-move for a given tour was the naive solution in time $O(n^k)$. At ICALP'16 de Berg, Buchin, Jansen and Woeginger showed an $O(n^{\\lfloor 2/3k \\rfloor+1})$-time algorithm.\n  We show an algorithm which r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05559","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.05559","created_at":"2026-05-18T00:39:06.714885+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.05559v2","created_at":"2026-05-18T00:39:06.714885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05559","created_at":"2026-05-18T00:39:06.714885+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4ASZ3ZKMP3N","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4ASZ3ZKMP3NHIB5","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4ASZ3ZK","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK","json":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK.json","graph_json":"https://pith.science/api/pith-number/J4ASZ3ZKMP3NHIB5KIB326QKFK/graph.json","events_json":"https://pith.science/api/pith-number/J4ASZ3ZKMP3NHIB5KIB326QKFK/events.json","paper":"https://pith.science/paper/J4ASZ3ZK"},"agent_actions":{"view_html":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK","download_json":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK.json","view_paper":"https://pith.science/paper/J4ASZ3ZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.05559&json=true","fetch_graph":"https://pith.science/api/pith-number/J4ASZ3ZKMP3NHIB5KIB326QKFK/graph.json","fetch_events":"https://pith.science/api/pith-number/J4ASZ3ZKMP3NHIB5KIB326QKFK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/action/storage_attestation","attest_author":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/action/author_attestation","sign_citation":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/action/citation_signature","submit_replication":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/action/replication_record"}},"created_at":"2026-05-18T00:39:06.714885+00:00","updated_at":"2026-05-18T00:39:06.714885+00:00"}