{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:J4ASZ3ZKMP3NHIB5KIB326QKFK","short_pith_number":"pith:J4ASZ3ZK","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"},"canonical_sha256":"4f012cef2a63f6d3a03d5203bd7a0a2a82dd75928796b051e0948b579661e7db","source":{"kind":"arxiv","id":"1703.05559","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05559","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05559v2","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05559","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"J4ASZ3ZKMP3N","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J4ASZ3ZKMP3NHIB5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J4ASZ3ZK","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:J4ASZ3ZKMP3NHIB5KIB326QKFK","target":"record","payload":{"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"},"canonical_sha256":"4f012cef2a63f6d3a03d5203bd7a0a2a82dd75928796b051e0948b579661e7db","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"},"source_kind":"arxiv","source_id":"1703.05559","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vnpMmNYBb/Iu8/ZFNEoOVT5gtbecQIaLopUmPm1TVhaxdIMSFvpZDny9vGYdlxXOc/kFvNEWQ42yN3QvPlY8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:10:06.608612Z"},"content_sha256":"ef64f14e6dc688e8984028e680bf4772bfb0a6bde2b4b13c6f647054113044ee","schema_version":"1.0","event_id":"sha256:ef64f14e6dc688e8984028e680bf4772bfb0a6bde2b4b13c6f647054113044ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:J4ASZ3ZKMP3NHIB5KIB326QKFK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3FQFgQoWa2MQwzVCv56AC/gsYz2wIbMUJVVjrQyocfQ65kZuIaPll+DGk0KeNQ04yqpa0g1gPSc1CQ059UHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:10:06.609270Z"},"content_sha256":"49823e3585747c26c6e9d2811daf87e1d76257209771770e4380bf2cb7fc51cd","schema_version":"1.0","event_id":"sha256:49823e3585747c26c6e9d2811daf87e1d76257209771770e4380bf2cb7fc51cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/bundle.json","state_url":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-18T23:10:06Z","links":{"resolver":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK","bundle":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/bundle.json","state":"https://pith.science/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4ASZ3ZKMP3NHIB5KIB326QKFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:J4ASZ3ZKMP3NHIB5KIB326QKFK","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":"cb0989038bb185c81a1691631db5148dbf7c4439073d04e0c9a270abaac35ae3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-16T11:09:25Z","title_canon_sha256":"4af6ae193a8b8cd34bee6b02a58e0d62c8d3e84dcaaa5136772227fe65a37fc1"},"schema_version":"1.0","source":{"id":"1703.05559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05559","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05559v2","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05559","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"J4ASZ3ZKMP3N","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J4ASZ3ZKMP3NHIB5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J4ASZ3ZK","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:49823e3585747c26c6e9d2811daf87e1d76257209771770e4380bf2cb7fc51cd","target":"graph","created_at":"2026-05-18T00:39:06Z","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 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","authors_text":"Arkadiusz Socala, Lukasz Kowalik, Marek Cygan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-16T11:09:25Z","title":"Improving TSP tours using dynamic programming over tree decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05559","kind":"arxiv","version":2},"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:ef64f14e6dc688e8984028e680bf4772bfb0a6bde2b4b13c6f647054113044ee","target":"record","created_at":"2026-05-18T00:39:06Z","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":"cb0989038bb185c81a1691631db5148dbf7c4439073d04e0c9a270abaac35ae3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-16T11:09:25Z","title_canon_sha256":"4af6ae193a8b8cd34bee6b02a58e0d62c8d3e84dcaaa5136772227fe65a37fc1"},"schema_version":"1.0","source":{"id":"1703.05559","kind":"arxiv","version":2}},"canonical_sha256":"4f012cef2a63f6d3a03d5203bd7a0a2a82dd75928796b051e0948b579661e7db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f012cef2a63f6d3a03d5203bd7a0a2a82dd75928796b051e0948b579661e7db","first_computed_at":"2026-05-18T00:39:06.714792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:06.714792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNCmdoB5GhPDvrYXP5vwFVYnbBESW/7wAHpd6i/9qzZwPBBMlzTywW6kPm/J5lx3GVDergnHPzYotJrLwBfaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:06.715414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef64f14e6dc688e8984028e680bf4772bfb0a6bde2b4b13c6f647054113044ee","sha256:49823e3585747c26c6e9d2811daf87e1d76257209771770e4380bf2cb7fc51cd"],"state_sha256":"12fa460c114dfcc1dee0eacec8f16d38f2c8a4f14d324b82f7f43839f17f62d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTjNab9xA4bPYgoh1BWA+8GBnCjFuKu0KB679ndFeyJwe06YF0RHCGL3bH2xZQieSOLptBda97Nr7orNuDH/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T23:10:06.611281Z","bundle_sha256":"df81a71758718997c87ef489274e57a5feba3d80c5a10bfee74ab89dab975d45"}}