{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YVSABPOBFDFTQQEM6UFT2ONCXA","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":"e21ad232e70698b8a97c48878bb536f634c74db9c43da60cae39d8eb76b05ec6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-12T19:14:47Z","title_canon_sha256":"110324da0e618f62ce092e53fed9ba30db6c84f9f69dc95873a207835a3490fb"},"schema_version":"1.0","source":{"id":"1612.03856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03856","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03856v1","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03856","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"YVSABPOBFDFT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YVSABPOBFDFTQQEM","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YVSABPOB","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:5d2174d392570a8f9a93b0d334e409055cdc19a387c7dfe26fbde13b5b91c6d1","target":"graph","created_at":"2026-05-18T00:55:18Z","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":"Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different $m$ vs. $n$ trade-off. For the case of $m = \\Theta(n^{1.5})$ the running time is $O(n^{2.47})$, just barely below $mn = \\Theta(n^{2.5})$. In this paper we simplify the previous algorithm using new algorithmic ideas an","authors_text":"Danupon Nanongkai, Monika Henzinger, Sebastian Krinninger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-12T19:14:47Z","title":"Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03856","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":"sha256:30f99e7db9d1e2c975d3f9b47b90c9d3b9be19cb8f8184b7d94c2f6d82a92a67","target":"record","created_at":"2026-05-18T00:55:18Z","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":"e21ad232e70698b8a97c48878bb536f634c74db9c43da60cae39d8eb76b05ec6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-12T19:14:47Z","title_canon_sha256":"110324da0e618f62ce092e53fed9ba30db6c84f9f69dc95873a207835a3490fb"},"schema_version":"1.0","source":{"id":"1612.03856","kind":"arxiv","version":1}},"canonical_sha256":"c56400bdc128cb38408cf50b3d39a2b8085e47cc5fce3aa42020d76af564673a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c56400bdc128cb38408cf50b3d39a2b8085e47cc5fce3aa42020d76af564673a","first_computed_at":"2026-05-18T00:55:18.201581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:18.201581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cxTKWWlUOlq05MWjWJXu0W0eM315ia+sOQMB6bR9BTHSDoziwF95ba9DSj6ihx+M8dWJilN4komVJptGnzWUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:18.202050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30f99e7db9d1e2c975d3f9b47b90c9d3b9be19cb8f8184b7d94c2f6d82a92a67","sha256:5d2174d392570a8f9a93b0d334e409055cdc19a387c7dfe26fbde13b5b91c6d1"],"state_sha256":"f2c8359b01563e93ac384865d7c3a0c578ec2100545a95c79091543c6963bce4"}