{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YBU6IWPBJV3JEWV37QASKJ3XKK","short_pith_number":"pith:YBU6IWPB","canonical_record":{"source":{"id":"1404.7307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-29T10:49:24Z","cross_cats_sorted":[],"title_canon_sha256":"0ecc848bf7ee062dafc67343e15c9406fa8a7063f3d6074b78c3e7cc9d100e62","abstract_canon_sha256":"eaa03c35509277408ee369dc57996abc7c13301f7f185d6eb61a3094701897df"},"schema_version":"1.0"},"canonical_sha256":"c069e459e14d76925abbfc0125277752a5e99ec95015e9a85eced94e6fa07925","source":{"kind":"arxiv","id":"1404.7307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7307","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7307v1","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7307","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"YBU6IWPBJV3J","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YBU6IWPBJV3JEWV3","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YBU6IWPB","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YBU6IWPBJV3JEWV37QASKJ3XKK","target":"record","payload":{"canonical_record":{"source":{"id":"1404.7307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-29T10:49:24Z","cross_cats_sorted":[],"title_canon_sha256":"0ecc848bf7ee062dafc67343e15c9406fa8a7063f3d6074b78c3e7cc9d100e62","abstract_canon_sha256":"eaa03c35509277408ee369dc57996abc7c13301f7f185d6eb61a3094701897df"},"schema_version":"1.0"},"canonical_sha256":"c069e459e14d76925abbfc0125277752a5e99ec95015e9a85eced94e6fa07925","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:56.904634Z","signature_b64":"GLVnUQw9ZrWqzEOFb5sxRH1pYGWm4czjo8ROm1ySumtvt49Ye+lb700tEJK78RTUWsFrvgCA7Jk+S7OvXrRGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c069e459e14d76925abbfc0125277752a5e99ec95015e9a85eced94e6fa07925","last_reissued_at":"2026-05-18T02:52:56.903937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:56.903937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.7307","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":"2026-05-18T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+y5NHZ3PkDKVnMVKVE+quToVzL7AfT12EMv4UiZpSazF/7aQffEhEFi1gVg6ly0kk3RIbajN6WPlUX3DAYq+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:46:03.790436Z"},"content_sha256":"a1247b5e99fc8f2e25b27e65f6986fd4a27e1c56dbb097e2a835d7d336f8fc74","schema_version":"1.0","event_id":"sha256:a1247b5e99fc8f2e25b27e65f6986fd4a27e1c56dbb097e2a835d7d336f8fc74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YBU6IWPBJV3JEWV37QASKJ3XKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Dynamic Graph Algorithms for Parameterized Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Keigo Oka, Yoichi Iwata","submitted_at":"2014-04-29T10:49:24Z","abstract_excerpt":"Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and query time are $o(|G|)$, that is, sublinear in the graph size. However, almost all such researches are for problems in P. In this paper, we investigate dynamic graphs for NP-hard problems exploiting the notion of fixed parameter tractability (FPT).\n  We give dynamic graphs for Vertex Cover and Cluste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7307","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":"2026-05-18T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4N0U/Q5/T0MnlMdu5oIMnwrocjfnU08hAUqjMle3k2Izu//jFTid7zEyJ+BaxI3jZpadtnXbC4dkOu5y5L47Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:46:03.790790Z"},"content_sha256":"e14f052a8b873039da7e9a63bbba7fd8a917a95f8976e85f191538657d311bc4","schema_version":"1.0","event_id":"sha256:e14f052a8b873039da7e9a63bbba7fd8a917a95f8976e85f191538657d311bc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBU6IWPBJV3JEWV37QASKJ3XKK/bundle.json","state_url":"https://pith.science/pith/YBU6IWPBJV3JEWV37QASKJ3XKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBU6IWPBJV3JEWV37QASKJ3XKK/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":"2026-05-30T15:46:03Z","links":{"resolver":"https://pith.science/pith/YBU6IWPBJV3JEWV37QASKJ3XKK","bundle":"https://pith.science/pith/YBU6IWPBJV3JEWV37QASKJ3XKK/bundle.json","state":"https://pith.science/pith/YBU6IWPBJV3JEWV37QASKJ3XKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBU6IWPBJV3JEWV37QASKJ3XKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YBU6IWPBJV3JEWV37QASKJ3XKK","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":"eaa03c35509277408ee369dc57996abc7c13301f7f185d6eb61a3094701897df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-29T10:49:24Z","title_canon_sha256":"0ecc848bf7ee062dafc67343e15c9406fa8a7063f3d6074b78c3e7cc9d100e62"},"schema_version":"1.0","source":{"id":"1404.7307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7307","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7307v1","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7307","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"YBU6IWPBJV3J","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YBU6IWPBJV3JEWV3","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YBU6IWPB","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:e14f052a8b873039da7e9a63bbba7fd8a917a95f8976e85f191538657d311bc4","target":"graph","created_at":"2026-05-18T02:52:56Z","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":"Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and query time are $o(|G|)$, that is, sublinear in the graph size. However, almost all such researches are for problems in P. In this paper, we investigate dynamic graphs for NP-hard problems exploiting the notion of fixed parameter tractability (FPT).\n  We give dynamic graphs for Vertex Cover and Cluste","authors_text":"Keigo Oka, Yoichi Iwata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-29T10:49:24Z","title":"Fast Dynamic Graph Algorithms for Parameterized Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7307","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:a1247b5e99fc8f2e25b27e65f6986fd4a27e1c56dbb097e2a835d7d336f8fc74","target":"record","created_at":"2026-05-18T02:52:56Z","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":"eaa03c35509277408ee369dc57996abc7c13301f7f185d6eb61a3094701897df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-29T10:49:24Z","title_canon_sha256":"0ecc848bf7ee062dafc67343e15c9406fa8a7063f3d6074b78c3e7cc9d100e62"},"schema_version":"1.0","source":{"id":"1404.7307","kind":"arxiv","version":1}},"canonical_sha256":"c069e459e14d76925abbfc0125277752a5e99ec95015e9a85eced94e6fa07925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c069e459e14d76925abbfc0125277752a5e99ec95015e9a85eced94e6fa07925","first_computed_at":"2026-05-18T02:52:56.903937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:56.903937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GLVnUQw9ZrWqzEOFb5sxRH1pYGWm4czjo8ROm1ySumtvt49Ye+lb700tEJK78RTUWsFrvgCA7Jk+S7OvXrRGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:56.904634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1247b5e99fc8f2e25b27e65f6986fd4a27e1c56dbb097e2a835d7d336f8fc74","sha256:e14f052a8b873039da7e9a63bbba7fd8a917a95f8976e85f191538657d311bc4"],"state_sha256":"b9e727dd9e8979ede6687b3404063041c558e2c01804037ba3ea40549fe41d8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zFB6X8J685WF3fCpfNbAPEDiP1B18JfgLp6vLfWGHhGVzf7uSKeXmixhDZtjkC/+PDc4ZcnZoFGhNxWO0BIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:46:03.792829Z","bundle_sha256":"a1f68a39814509051375b4a2f1b8c2034a66edbad0af3cf809080a7d77a60b1d"}}