{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NQZJEODG7AW7ATYFB5LOOMYWMS","short_pith_number":"pith:NQZJEODG","schema_version":"1.0","canonical_sha256":"6c32923866f82df04f050f56e7331664b19114568b527637deba3b2d7bcc6aa0","source":{"kind":"arxiv","id":"1610.06934","version":3},"attestation_state":"computed","paper":{"title":"The K Shortest Paths Problem with Application to Routing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"David Burstein, Leigh Metcalf","submitted_at":"2016-10-21T20:02:53Z","abstract_excerpt":"Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted real-world networks. First, we present an easy to implement $O(m\\log m+kL)$ solution for finding all (nonbacktracking) paths with bounded length $D$ between two arbitrary nodes on a positively weighted graph, where $L$ is an upperbound for the number of nodes in any of the $k$ outputted paths. Subsequently, we illustrate that for undirected Chung-Lu random graphs"},"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":"1610.06934","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-21T20:02:53Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"a7ec4459cb8ca0b55887a029e2beb6b112972d846b60eb0fdc64562e9d887621","abstract_canon_sha256":"f88027e630d90d67e27fcc7a0d5249c3ebfc332bc0b2b4a632fca9450fe215ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:13.778101Z","signature_b64":"M8ePPpwTtaeULfI3iyDjXyWpsiXOYZOi7HZJSHDwztkHXKdLdDlnwlTMFSFYZgRXRYuPKBs7GRCY4edfDV2fAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c32923866f82df04f050f56e7331664b19114568b527637deba3b2d7bcc6aa0","last_reissued_at":"2026-05-18T00:31:13.777380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:13.777380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The K Shortest Paths Problem with Application to Routing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"David Burstein, Leigh Metcalf","submitted_at":"2016-10-21T20:02:53Z","abstract_excerpt":"Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted real-world networks. First, we present an easy to implement $O(m\\log m+kL)$ solution for finding all (nonbacktracking) paths with bounded length $D$ between two arbitrary nodes on a positively weighted graph, where $L$ is an upperbound for the number of nodes in any of the $k$ outputted paths. Subsequently, we illustrate that for undirected Chung-Lu random graphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06934","kind":"arxiv","version":3},"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":"1610.06934","created_at":"2026-05-18T00:31:13.777473+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06934v3","created_at":"2026-05-18T00:31:13.777473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06934","created_at":"2026-05-18T00:31:13.777473+00:00"},{"alias_kind":"pith_short_12","alias_value":"NQZJEODG7AW7","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"NQZJEODG7AW7ATYF","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"NQZJEODG","created_at":"2026-05-18T12:30:36.002864+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/NQZJEODG7AW7ATYFB5LOOMYWMS","json":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS.json","graph_json":"https://pith.science/api/pith-number/NQZJEODG7AW7ATYFB5LOOMYWMS/graph.json","events_json":"https://pith.science/api/pith-number/NQZJEODG7AW7ATYFB5LOOMYWMS/events.json","paper":"https://pith.science/paper/NQZJEODG"},"agent_actions":{"view_html":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS","download_json":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS.json","view_paper":"https://pith.science/paper/NQZJEODG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06934&json=true","fetch_graph":"https://pith.science/api/pith-number/NQZJEODG7AW7ATYFB5LOOMYWMS/graph.json","fetch_events":"https://pith.science/api/pith-number/NQZJEODG7AW7ATYFB5LOOMYWMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS/action/storage_attestation","attest_author":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS/action/author_attestation","sign_citation":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS/action/citation_signature","submit_replication":"https://pith.science/pith/NQZJEODG7AW7ATYFB5LOOMYWMS/action/replication_record"}},"created_at":"2026-05-18T00:31:13.777473+00:00","updated_at":"2026-05-18T00:31:13.777473+00:00"}