{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SARBJWVRTIWFV2EXRXVL5WVLH3","short_pith_number":"pith:SARBJWVR","canonical_record":{"source":{"id":"1509.03976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-14T07:50:27Z","cross_cats_sorted":["cs.CC","cs.DM","math.CO","math.OC"],"title_canon_sha256":"23ee0321df1f02c67b4e6ff657d158fde25d94024416a5ae8ea7d04ffd02e314","abstract_canon_sha256":"16b90f162012862cfa06795375dd1bea4992f82843506dc12d40724e4ee0a78d"},"schema_version":"1.0"},"canonical_sha256":"902214dab19a2c5ae8978deabedaab3ee5310b3d7be28424aaed3a6a3b54cdc8","source":{"kind":"arxiv","id":"1509.03976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03976","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03976v1","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03976","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"SARBJWVRTIWF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SARBJWVRTIWFV2EX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SARBJWVR","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SARBJWVRTIWFV2EXRXVL5WVLH3","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-14T07:50:27Z","cross_cats_sorted":["cs.CC","cs.DM","math.CO","math.OC"],"title_canon_sha256":"23ee0321df1f02c67b4e6ff657d158fde25d94024416a5ae8ea7d04ffd02e314","abstract_canon_sha256":"16b90f162012862cfa06795375dd1bea4992f82843506dc12d40724e4ee0a78d"},"schema_version":"1.0"},"canonical_sha256":"902214dab19a2c5ae8978deabedaab3ee5310b3d7be28424aaed3a6a3b54cdc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:08.587601Z","signature_b64":"wkEroT4yipg3PVIFLFStmFaiFoeHmWFDXWbH1EUnNtVErYMsibPtaiZrRySryHM6Yux+aRGgU8GsZ1wcZ8lrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"902214dab19a2c5ae8978deabedaab3ee5310b3d7be28424aaed3a6a3b54cdc8","last_reissued_at":"2026-05-18T01:33:08.587088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:08.587088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03976","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uA57FG8bAjmxmAc3OI6Y05gdNqnnPSMcUeV9fwDN3IaKxJfmuvtCOekcHiFhJt1fpXs7kpXOymvx7dTuC6a/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:53:47.421871Z"},"content_sha256":"48774913088e02b1c95d5e7b2cb8ee8eb99bc1b3383937390611607c4f5c2df5","schema_version":"1.0","event_id":"sha256:48774913088e02b1c95d5e7b2cb8ee8eb99bc1b3383937390611607c4f5c2df5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SARBJWVRTIWFV2EXRXVL5WVLH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximability of TSP on Power Law Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO","math.OC"],"primary_cat":"cs.DS","authors_text":"Marek Karpinski, Mathias Hauptmann, Mikael Gast","submitted_at":"2015-09-14T07:50:27Z","abstract_excerpt":"In this paper we study the special case of Graphic TSP where the underlying graph is a power law graph (PLG). We give a refined analysis of some of the current best approximation algorithms and show that an improved approximation ratio can be achieved for certain ranges of the power law exponent $\\beta$. For the value of power law exponent $\\beta=1.5$ we obtain an approximation ratio of $1.34$ for Graphic TSP. Moreover we study the $(1,2)$-TSP with the underlying graph of $1$-edges being a PLG. We show improved approximation ratios in the case of underlying deterministic PLGs for $\\beta$ great"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03976","kind":"arxiv","version":1},"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":"2026-05-18T01:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2um0ZJqnMKSwG3wRt/+8QLJQnBoLQez4iggL8wzRPRRQAxjYi2Hw4l+wq+pgq+Hg2frO/c00OJdeMZPFlnFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:53:47.422218Z"},"content_sha256":"08d3e877baca4a357bb09ad8f35112db3a7159d24816722d8f2dbfaf0096fc39","schema_version":"1.0","event_id":"sha256:08d3e877baca4a357bb09ad8f35112db3a7159d24816722d8f2dbfaf0096fc39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SARBJWVRTIWFV2EXRXVL5WVLH3/bundle.json","state_url":"https://pith.science/pith/SARBJWVRTIWFV2EXRXVL5WVLH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SARBJWVRTIWFV2EXRXVL5WVLH3/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":"2026-05-28T14:53:47Z","links":{"resolver":"https://pith.science/pith/SARBJWVRTIWFV2EXRXVL5WVLH3","bundle":"https://pith.science/pith/SARBJWVRTIWFV2EXRXVL5WVLH3/bundle.json","state":"https://pith.science/pith/SARBJWVRTIWFV2EXRXVL5WVLH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SARBJWVRTIWFV2EXRXVL5WVLH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SARBJWVRTIWFV2EXRXVL5WVLH3","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":"16b90f162012862cfa06795375dd1bea4992f82843506dc12d40724e4ee0a78d","cross_cats_sorted":["cs.CC","cs.DM","math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-14T07:50:27Z","title_canon_sha256":"23ee0321df1f02c67b4e6ff657d158fde25d94024416a5ae8ea7d04ffd02e314"},"schema_version":"1.0","source":{"id":"1509.03976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03976","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03976v1","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03976","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"SARBJWVRTIWF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SARBJWVRTIWFV2EX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SARBJWVR","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:08d3e877baca4a357bb09ad8f35112db3a7159d24816722d8f2dbfaf0096fc39","target":"graph","created_at":"2026-05-18T01:33:08Z","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":"In this paper we study the special case of Graphic TSP where the underlying graph is a power law graph (PLG). We give a refined analysis of some of the current best approximation algorithms and show that an improved approximation ratio can be achieved for certain ranges of the power law exponent $\\beta$. For the value of power law exponent $\\beta=1.5$ we obtain an approximation ratio of $1.34$ for Graphic TSP. Moreover we study the $(1,2)$-TSP with the underlying graph of $1$-edges being a PLG. We show improved approximation ratios in the case of underlying deterministic PLGs for $\\beta$ great","authors_text":"Marek Karpinski, Mathias Hauptmann, Mikael Gast","cross_cats":["cs.CC","cs.DM","math.CO","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-14T07:50:27Z","title":"Approximability of TSP on Power Law Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03976","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":"sha256:48774913088e02b1c95d5e7b2cb8ee8eb99bc1b3383937390611607c4f5c2df5","target":"record","created_at":"2026-05-18T01:33:08Z","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":"16b90f162012862cfa06795375dd1bea4992f82843506dc12d40724e4ee0a78d","cross_cats_sorted":["cs.CC","cs.DM","math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-14T07:50:27Z","title_canon_sha256":"23ee0321df1f02c67b4e6ff657d158fde25d94024416a5ae8ea7d04ffd02e314"},"schema_version":"1.0","source":{"id":"1509.03976","kind":"arxiv","version":1}},"canonical_sha256":"902214dab19a2c5ae8978deabedaab3ee5310b3d7be28424aaed3a6a3b54cdc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"902214dab19a2c5ae8978deabedaab3ee5310b3d7be28424aaed3a6a3b54cdc8","first_computed_at":"2026-05-18T01:33:08.587088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:08.587088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkEroT4yipg3PVIFLFStmFaiFoeHmWFDXWbH1EUnNtVErYMsibPtaiZrRySryHM6Yux+aRGgU8GsZ1wcZ8lrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:08.587601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48774913088e02b1c95d5e7b2cb8ee8eb99bc1b3383937390611607c4f5c2df5","sha256:08d3e877baca4a357bb09ad8f35112db3a7159d24816722d8f2dbfaf0096fc39"],"state_sha256":"19d8bb884896aa9653097dc1dfad45c0ec46cce437a95892e22b39962900bb64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLDyTbZ2x1YiAtrZMCQZfdrC35ij9abGTuV6kRY709SF39Uc1aYbewjkeCi09qMoksjgmYtRAS38vCPsNNtyAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:53:47.424328Z","bundle_sha256":"ad511d2785776ab9f81e041ac4fc05ea30ed17a3cc0afb5815cc67925f0eb8c5"}}