{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KKZIBDUB4USIJGHWGWQ4Q5DPO3","short_pith_number":"pith:KKZIBDUB","schema_version":"1.0","canonical_sha256":"52b2808e81e5248498f635a1c8746f76f1a8155292b23ea0765b70041e97342f","source":{"kind":"arxiv","id":"1609.01373","version":1},"attestation_state":"computed","paper":{"title":"Improved Algorithms for Computing $k$-Sink on Dynamic Path Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Binay Bhattacharya, Mordecai J. Golin, Naoki Katoh, Tsunehiko Kameda, Yuya Higashikawa","submitted_at":"2016-09-06T02:19:29Z","abstract_excerpt":"We present a novel approach to finding the $k$-sink on dynamic path networks with general edge capacities. Our first algorithm runs in $O(n \\log n + k^2 \\log^4 n)$ time, where $n$ is the number of vertices on the given path, and our second algorithm runs in $O(n \\log^3 n)$ time. Together, they improve upon the previously most efficient $O(kn \\log^2 n)$ time algorithm due to Arumugam et al. for all values of $k$. In the case where all the edges have the same capacity, we again present two algorithms that run in $O(n + k^2 \\log^2n)$ time and $O(n \\log n)$ time, respectively, and they together im"},"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":"1609.01373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-06T02:19:29Z","cross_cats_sorted":[],"title_canon_sha256":"baff0d215a1694c5a1b1ffe95ccc77a2164f6bb488b7050310a4facc60d33436","abstract_canon_sha256":"c189610696470a481cf8797a56d04cfa75500b7b44616552ca84341629d1be86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:39.753639Z","signature_b64":"5kvAYpfk5bK84cP/U2PLkMtgUoQl4LJCRSiPYSuAmKq5nYZSRSgP8Qer1rJXLnqNRYYgzBMDmR2CpHRSQ2X/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52b2808e81e5248498f635a1c8746f76f1a8155292b23ea0765b70041e97342f","last_reissued_at":"2026-05-18T01:05:39.753198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:39.753198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Algorithms for Computing $k$-Sink on Dynamic Path Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Binay Bhattacharya, Mordecai J. Golin, Naoki Katoh, Tsunehiko Kameda, Yuya Higashikawa","submitted_at":"2016-09-06T02:19:29Z","abstract_excerpt":"We present a novel approach to finding the $k$-sink on dynamic path networks with general edge capacities. Our first algorithm runs in $O(n \\log n + k^2 \\log^4 n)$ time, where $n$ is the number of vertices on the given path, and our second algorithm runs in $O(n \\log^3 n)$ time. Together, they improve upon the previously most efficient $O(kn \\log^2 n)$ time algorithm due to Arumugam et al. for all values of $k$. In the case where all the edges have the same capacity, we again present two algorithms that run in $O(n + k^2 \\log^2n)$ time and $O(n \\log n)$ time, respectively, and they together im"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01373","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.01373","created_at":"2026-05-18T01:05:39.753273+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01373v1","created_at":"2026-05-18T01:05:39.753273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01373","created_at":"2026-05-18T01:05:39.753273+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKZIBDUB4USI","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKZIBDUB4USIJGHW","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKZIBDUB","created_at":"2026-05-18T12:30:25.849896+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/KKZIBDUB4USIJGHWGWQ4Q5DPO3","json":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3.json","graph_json":"https://pith.science/api/pith-number/KKZIBDUB4USIJGHWGWQ4Q5DPO3/graph.json","events_json":"https://pith.science/api/pith-number/KKZIBDUB4USIJGHWGWQ4Q5DPO3/events.json","paper":"https://pith.science/paper/KKZIBDUB"},"agent_actions":{"view_html":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3","download_json":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3.json","view_paper":"https://pith.science/paper/KKZIBDUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01373&json=true","fetch_graph":"https://pith.science/api/pith-number/KKZIBDUB4USIJGHWGWQ4Q5DPO3/graph.json","fetch_events":"https://pith.science/api/pith-number/KKZIBDUB4USIJGHWGWQ4Q5DPO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3/action/storage_attestation","attest_author":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3/action/author_attestation","sign_citation":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3/action/citation_signature","submit_replication":"https://pith.science/pith/KKZIBDUB4USIJGHWGWQ4Q5DPO3/action/replication_record"}},"created_at":"2026-05-18T01:05:39.753273+00:00","updated_at":"2026-05-18T01:05:39.753273+00:00"}