{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EBJQQ3RX5CUQHWVSKHTHOWZEEC","short_pith_number":"pith:EBJQQ3RX","schema_version":"1.0","canonical_sha256":"2053086e37e8a903dab251e6775b2420b4858a1c0b69c6e0899dfaaad419e0bb","source":{"kind":"arxiv","id":"1509.05896","version":2},"attestation_state":"computed","paper":{"title":"On space efficiency of algorithms working on structural decompositions of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Marcin Wrochna, Micha{\\l} Pilipczuk","submitted_at":"2015-09-19T14:20:05Z","abstract_excerpt":"Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the decomposition's width. Following the work of Allender et al. [Theory of Computing, '14], we investigate whether this space complexity explosion is unavoidable. Using the idea of reparameterization of Cai and Juedes [J. Comput. Syst. Sci., '03], we prove that the question is closely related to a conjecture that the Longest Common Subsequence problem parameterized "},"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":"1509.05896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-09-19T14:20:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"b31e02921cffb2d3c8f89be91f746a546b216e9fec1b807d67c1746e9874c4f4","abstract_canon_sha256":"2da3c4c546557f589d3403c240e8827f14c4aee6f8fdf56e7333c95ee5746daf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:00.310938Z","signature_b64":"qR+dYXD7ialcWFokHdp+8bCDUAbQ5Xx8riVI/xgjX7iSQV/XdCE8omK31CVPx6OJ5TpAX9CA4kCthdJ71Ey0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2053086e37e8a903dab251e6775b2420b4858a1c0b69c6e0899dfaaad419e0bb","last_reissued_at":"2026-05-18T01:15:00.310478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:00.310478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On space efficiency of algorithms working on structural decompositions of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Marcin Wrochna, Micha{\\l} Pilipczuk","submitted_at":"2015-09-19T14:20:05Z","abstract_excerpt":"Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the decomposition's width. Following the work of Allender et al. [Theory of Computing, '14], we investigate whether this space complexity explosion is unavoidable. Using the idea of reparameterization of Cai and Juedes [J. Comput. Syst. Sci., '03], we prove that the question is closely related to a conjecture that the Longest Common Subsequence problem parameterized "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05896","kind":"arxiv","version":2},"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":"1509.05896","created_at":"2026-05-18T01:15:00.310548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05896v2","created_at":"2026-05-18T01:15:00.310548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05896","created_at":"2026-05-18T01:15:00.310548+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBJQQ3RX5CUQ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBJQQ3RX5CUQHWVS","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBJQQ3RX","created_at":"2026-05-18T12:29:19.899920+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/EBJQQ3RX5CUQHWVSKHTHOWZEEC","json":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC.json","graph_json":"https://pith.science/api/pith-number/EBJQQ3RX5CUQHWVSKHTHOWZEEC/graph.json","events_json":"https://pith.science/api/pith-number/EBJQQ3RX5CUQHWVSKHTHOWZEEC/events.json","paper":"https://pith.science/paper/EBJQQ3RX"},"agent_actions":{"view_html":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC","download_json":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC.json","view_paper":"https://pith.science/paper/EBJQQ3RX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05896&json=true","fetch_graph":"https://pith.science/api/pith-number/EBJQQ3RX5CUQHWVSKHTHOWZEEC/graph.json","fetch_events":"https://pith.science/api/pith-number/EBJQQ3RX5CUQHWVSKHTHOWZEEC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC/action/storage_attestation","attest_author":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC/action/author_attestation","sign_citation":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC/action/citation_signature","submit_replication":"https://pith.science/pith/EBJQQ3RX5CUQHWVSKHTHOWZEEC/action/replication_record"}},"created_at":"2026-05-18T01:15:00.310548+00:00","updated_at":"2026-05-18T01:15:00.310548+00:00"}