{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:L63KY2KYYIH3NPJX2TSJCSXOHR","short_pith_number":"pith:L63KY2KY","schema_version":"1.0","canonical_sha256":"5fb6ac6958c20fb6bd37d4e4914aee3c74afa47bfc5f85bf65427f4746362f6e","source":{"kind":"arxiv","id":"1111.6745","version":6},"attestation_state":"computed","paper":{"title":"Fast Balanced Partitioning is Hard, Even on Grids and Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Andreas Emil Feldmann","submitted_at":"2011-11-29T10:07:18Z","abstract_excerpt":"Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that this tradeoff between runtime and solution quality is necessary. For the problem a minimum number of edges in a graph need to be found that, when cut, partition the vertices into k equal-sized sets. We develop a reduction framework which identifies some necessary conditions on the considered graph class in order to prove the hardness of the problem. We focus "},"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":"1111.6745","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-11-29T10:07:18Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"7f1437a6304d247e8c77afde37836117e870e92bb92a9b4cd05ed7c272a7c163","abstract_canon_sha256":"7cf3844da9e302e63f5854791397bcdfb36b81c15b657a0d4c8762f3bacd9dc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:44.699261Z","signature_b64":"9VPHKA/kCQ5Xn5K8XlUEanMbyFgJX5D4o8/kh9MDnpWjbENl9SJ4+BZn+0Wfg654iBTOh7ywnxxDzAwglNPJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fb6ac6958c20fb6bd37d4e4914aee3c74afa47bfc5f85bf65427f4746362f6e","last_reissued_at":"2026-05-17T23:47:44.698788Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:44.698788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Balanced Partitioning is Hard, Even on Grids and Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Andreas Emil Feldmann","submitted_at":"2011-11-29T10:07:18Z","abstract_excerpt":"Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that this tradeoff between runtime and solution quality is necessary. For the problem a minimum number of edges in a graph need to be found that, when cut, partition the vertices into k equal-sized sets. We develop a reduction framework which identifies some necessary conditions on the considered graph class in order to prove the hardness of the problem. We focus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6745","kind":"arxiv","version":6},"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":"1111.6745","created_at":"2026-05-17T23:47:44.698860+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6745v6","created_at":"2026-05-17T23:47:44.698860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6745","created_at":"2026-05-17T23:47:44.698860+00:00"},{"alias_kind":"pith_short_12","alias_value":"L63KY2KYYIH3","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"L63KY2KYYIH3NPJX","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"L63KY2KY","created_at":"2026-05-18T12:26:34.985390+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/L63KY2KYYIH3NPJX2TSJCSXOHR","json":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR.json","graph_json":"https://pith.science/api/pith-number/L63KY2KYYIH3NPJX2TSJCSXOHR/graph.json","events_json":"https://pith.science/api/pith-number/L63KY2KYYIH3NPJX2TSJCSXOHR/events.json","paper":"https://pith.science/paper/L63KY2KY"},"agent_actions":{"view_html":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR","download_json":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR.json","view_paper":"https://pith.science/paper/L63KY2KY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6745&json=true","fetch_graph":"https://pith.science/api/pith-number/L63KY2KYYIH3NPJX2TSJCSXOHR/graph.json","fetch_events":"https://pith.science/api/pith-number/L63KY2KYYIH3NPJX2TSJCSXOHR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR/action/storage_attestation","attest_author":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR/action/author_attestation","sign_citation":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR/action/citation_signature","submit_replication":"https://pith.science/pith/L63KY2KYYIH3NPJX2TSJCSXOHR/action/replication_record"}},"created_at":"2026-05-17T23:47:44.698860+00:00","updated_at":"2026-05-17T23:47:44.698860+00:00"}