{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HUSYQE5F6AQLCHK4PSSZAXRTR6","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":"56cd7ff3bc40e48874876c7232909ea2f734c00ad2513a8c39ff61e6a11f8360","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-03T18:04:34Z","title_canon_sha256":"d0ad9bf4d321a3ca99c65e0a9955058f61eae13187865124bdc3e49dd7dedfc1"},"schema_version":"1.0","source":{"id":"1905.01325","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01325","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01325v2","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01325","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"HUSYQE5F6AQL","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HUSYQE5F6AQLCHK4","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HUSYQE5F","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:f4ff7aa3e6996f9f7a6fab479dcfd82ffbcdf5dfa0d3be2ce2ff471de18429ca","target":"graph","created_at":"2026-05-17T23:43:08Z","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 give a single-source shortest-path algorithm that breaks, after over 60 years, the $O(n \\cdot m)$ time bound for the Bellman-Ford algorithm, where $n$ is the number of vertices and $m$ is the number of arcs of the graph. Our algorithm converts the input graph to a graph with nonnegative weights by performing at most $\\min(\\sqrt{n},\\sqrt{m/\\log n})$ calls to Dijkstra's algorithm, such that the shortest-path tree is the same for the new graph as that for the original. When Dijkstra's algorithm is implemented using Fibonacci heaps, the running time of our algorithm is therefore $","authors_text":"Amr Elmasry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-03T18:04:34Z","title":"Breaking the Bellman-Ford Shortest-Path Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01325","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":"sha256:95f044d50ad460778bb57f06551f2e64f903f6f93df19a30a26d6fd9880ff43a","target":"record","created_at":"2026-05-17T23:43:08Z","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":"56cd7ff3bc40e48874876c7232909ea2f734c00ad2513a8c39ff61e6a11f8360","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-03T18:04:34Z","title_canon_sha256":"d0ad9bf4d321a3ca99c65e0a9955058f61eae13187865124bdc3e49dd7dedfc1"},"schema_version":"1.0","source":{"id":"1905.01325","kind":"arxiv","version":2}},"canonical_sha256":"3d258813a5f020b11d5c7ca5905e338faaa8ade17aef2dd156bf29df2a2ca3ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d258813a5f020b11d5c7ca5905e338faaa8ade17aef2dd156bf29df2a2ca3ee","first_computed_at":"2026-05-17T23:43:08.870211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:08.870211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QqRZOYcr4KZMQgRYzSrefaSZN6jd5mZH/SOK3/6XcHoQD+8bvYbyOwncJ8PwOm1ysq9vZ1GMqzyXt6B7AyQ0BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:08.870652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01325","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95f044d50ad460778bb57f06551f2e64f903f6f93df19a30a26d6fd9880ff43a","sha256:f4ff7aa3e6996f9f7a6fab479dcfd82ffbcdf5dfa0d3be2ce2ff471de18429ca"],"state_sha256":"5607f2735c8a89c85152aac280c0706291dcef9cd16c140ba32613b627dac6fc"}