{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3W3RL2OS6GXJFNOPNXHOMFTBSW","short_pith_number":"pith:3W3RL2OS","canonical_record":{"source":{"id":"1003.5330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-27T22:46:05Z","cross_cats_sorted":[],"title_canon_sha256":"3caebcf2960191dbfd4ca5a3b5797e5178a97889b4af5b5347566defcb462903","abstract_canon_sha256":"164ec6c981a8319961ed4ce7abe128224186bee3a4577b131eba6790cd18e1a1"},"schema_version":"1.0"},"canonical_sha256":"ddb715e9d2f1ae92b5cf6dcee6166195a6798d8704c63aa86747d1949228ccab","source":{"kind":"arxiv","id":"1003.5330","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5330","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5330v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5330","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"3W3RL2OS6GXJ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3W3RL2OS6GXJFNOP","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3W3RL2OS","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3W3RL2OS6GXJFNOPNXHOMFTBSW","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-27T22:46:05Z","cross_cats_sorted":[],"title_canon_sha256":"3caebcf2960191dbfd4ca5a3b5797e5178a97889b4af5b5347566defcb462903","abstract_canon_sha256":"164ec6c981a8319961ed4ce7abe128224186bee3a4577b131eba6790cd18e1a1"},"schema_version":"1.0"},"canonical_sha256":"ddb715e9d2f1ae92b5cf6dcee6166195a6798d8704c63aa86747d1949228ccab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:25.359907Z","signature_b64":"nkT+k0p1N88uvFVbCa/z4e38yRVQh6R/XH5aCCd1uuGPrq8TpCNzBu+H+Ea29mg580iwqJn8AaxSIahRK0sNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddb715e9d2f1ae92b5cf6dcee6166195a6798d8704c63aa86747d1949228ccab","last_reissued_at":"2026-05-18T04:02:25.359479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:25.359479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5330","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtiQllpbb3ueBjaVI5YoKPpN2QAMfQHSpftfCjnAoSElgYYEBelLVGpAZGyQovAQNTtQvy2A6AbU9nRWu6mCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:38:38.610330Z"},"content_sha256":"f959473c1486c22b31ef2e518cafb32a60b00f0c45af355eeec579540076a1ee","schema_version":"1.0","event_id":"sha256:f959473c1486c22b31ef2e518cafb32a60b00f0c45af355eeec579540076a1ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3W3RL2OS6GXJFNOPNXHOMFTBSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Daniel Karapetyan, Gregory Gutin","submitted_at":"2010-03-27T22:46:05Z","abstract_excerpt":"The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5330","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"We/QCLsOAM7QiZ5uluVbZHjQxPznzRbTD2p9mxhpEJnaiCh/fZx+zgcxKjp4/7u/ZinJiNYY9uyektmusTYAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:38:38.610799Z"},"content_sha256":"878a29620080c1da8292e3ca2e0986e3a94a652031a4a4f9df46ebb61fa79d80","schema_version":"1.0","event_id":"sha256:878a29620080c1da8292e3ca2e0986e3a94a652031a4a4f9df46ebb61fa79d80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW/bundle.json","state_url":"https://pith.science/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW/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":"2026-06-23T17:38:38Z","links":{"resolver":"https://pith.science/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW","bundle":"https://pith.science/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW/bundle.json","state":"https://pith.science/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3W3RL2OS6GXJFNOPNXHOMFTBSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3W3RL2OS6GXJFNOPNXHOMFTBSW","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":"164ec6c981a8319961ed4ce7abe128224186bee3a4577b131eba6790cd18e1a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-27T22:46:05Z","title_canon_sha256":"3caebcf2960191dbfd4ca5a3b5797e5178a97889b4af5b5347566defcb462903"},"schema_version":"1.0","source":{"id":"1003.5330","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5330","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5330v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5330","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"3W3RL2OS6GXJ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3W3RL2OS6GXJFNOP","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3W3RL2OS","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:878a29620080c1da8292e3ca2e0986e3a94a652031a4a4f9df46ebb61fa79d80","target":"graph","created_at":"2026-05-18T04:02:25Z","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":"The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of ","authors_text":"Daniel Karapetyan, Gregory Gutin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-27T22:46:05Z","title":"Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5330","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:f959473c1486c22b31ef2e518cafb32a60b00f0c45af355eeec579540076a1ee","target":"record","created_at":"2026-05-18T04:02:25Z","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":"164ec6c981a8319961ed4ce7abe128224186bee3a4577b131eba6790cd18e1a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-27T22:46:05Z","title_canon_sha256":"3caebcf2960191dbfd4ca5a3b5797e5178a97889b4af5b5347566defcb462903"},"schema_version":"1.0","source":{"id":"1003.5330","kind":"arxiv","version":2}},"canonical_sha256":"ddb715e9d2f1ae92b5cf6dcee6166195a6798d8704c63aa86747d1949228ccab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddb715e9d2f1ae92b5cf6dcee6166195a6798d8704c63aa86747d1949228ccab","first_computed_at":"2026-05-18T04:02:25.359479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:25.359479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkT+k0p1N88uvFVbCa/z4e38yRVQh6R/XH5aCCd1uuGPrq8TpCNzBu+H+Ea29mg580iwqJn8AaxSIahRK0sNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:25.359907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f959473c1486c22b31ef2e518cafb32a60b00f0c45af355eeec579540076a1ee","sha256:878a29620080c1da8292e3ca2e0986e3a94a652031a4a4f9df46ebb61fa79d80"],"state_sha256":"bd255c657f9e432892c9db6fd48cc8912fc370cb7f79fafce394582252942a0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVSORyu4csosdFFIXZACc0FgDj7i6ETs9fRzC9BTTxNV6hNWZwx4XxkuANJtlfVrKjiTiJbdGW1W3RNqVB4NDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:38:38.613340Z","bundle_sha256":"ee40aa32ad763a8a1e83c90ff78526a74a8b1656382bd5134dbf0bd2489ad828"}}