{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PQLQGITTPT5YWLNZWWV56BYAUN","short_pith_number":"pith:PQLQGITT","schema_version":"1.0","canonical_sha256":"7c170322737cfb8b2db9b5abdf0700a34aa79e2ce2aef5c1aa9f72de9407d29a","source":{"kind":"arxiv","id":"1710.08488","version":1},"attestation_state":"computed","paper":{"title":"An FPT Algorithm Beating 2-Approximation for $k$-Cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, Euiwoong Lee, Jason Li","submitted_at":"2017-10-23T20:10:40Z","abstract_excerpt":"In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h \\in [2,k]$, a $(2-h/k)$-approximation algorithm for $k$-cut that runs in time $n^{O(h)}$. Hence to get a $(2 - \\varepsilon)$-approximation algorithm for some absolute constant $\\varepsilon$, the best runtime using prior techniques is $n^{O(k\\varepsilon)}$. Moreover, it was recently shown that getting a $(2 - \\varepsilon)$-approximation for general $k$ is NP-"},"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":"1710.08488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-23T20:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"6fabc46a074b36ad90bc726ff944aa039ef2263ce92de69f491f73ea4adc320f","abstract_canon_sha256":"9f82fd876bef97055aec5a948aeac3e85ee1ecb643eebabe1e2d60322fc8ce0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:15.890122Z","signature_b64":"s7eOtmhSDvGmKs8VaqfNdfQjFZAgTjVLBihlW76lvkNhBDQhOQJI4oLPLmSvVRmjZnJTeGRLyfrvspLAIpxTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c170322737cfb8b2db9b5abdf0700a34aa79e2ce2aef5c1aa9f72de9407d29a","last_reissued_at":"2026-05-18T00:32:15.889333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:15.889333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An FPT Algorithm Beating 2-Approximation for $k$-Cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, Euiwoong Lee, Jason Li","submitted_at":"2017-10-23T20:10:40Z","abstract_excerpt":"In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h \\in [2,k]$, a $(2-h/k)$-approximation algorithm for $k$-cut that runs in time $n^{O(h)}$. Hence to get a $(2 - \\varepsilon)$-approximation algorithm for some absolute constant $\\varepsilon$, the best runtime using prior techniques is $n^{O(k\\varepsilon)}$. Moreover, it was recently shown that getting a $(2 - \\varepsilon)$-approximation for general $k$ is NP-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08488","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":"1710.08488","created_at":"2026-05-18T00:32:15.889454+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.08488v1","created_at":"2026-05-18T00:32:15.889454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08488","created_at":"2026-05-18T00:32:15.889454+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQLQGITTPT5Y","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQLQGITTPT5YWLNZ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQLQGITT","created_at":"2026-05-18T12:31:37.085036+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/PQLQGITTPT5YWLNZWWV56BYAUN","json":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN.json","graph_json":"https://pith.science/api/pith-number/PQLQGITTPT5YWLNZWWV56BYAUN/graph.json","events_json":"https://pith.science/api/pith-number/PQLQGITTPT5YWLNZWWV56BYAUN/events.json","paper":"https://pith.science/paper/PQLQGITT"},"agent_actions":{"view_html":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN","download_json":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN.json","view_paper":"https://pith.science/paper/PQLQGITT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.08488&json=true","fetch_graph":"https://pith.science/api/pith-number/PQLQGITTPT5YWLNZWWV56BYAUN/graph.json","fetch_events":"https://pith.science/api/pith-number/PQLQGITTPT5YWLNZWWV56BYAUN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN/action/storage_attestation","attest_author":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN/action/author_attestation","sign_citation":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN/action/citation_signature","submit_replication":"https://pith.science/pith/PQLQGITTPT5YWLNZWWV56BYAUN/action/replication_record"}},"created_at":"2026-05-18T00:32:15.889454+00:00","updated_at":"2026-05-18T00:32:15.889454+00:00"}