{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QPIEJKGRM7S7DO2RWNWSG77NGP","short_pith_number":"pith:QPIEJKGR","canonical_record":{"source":{"id":"1308.2858","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-13T13:22:02Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"33cc7e9a94d00e541e9d64f6004a3a4ab5d0a25fece9bc588201d249aa6baf36","abstract_canon_sha256":"1e30319d31f242515d7080555fd42d5d42e114c63e220b020fd42b32fbe71b28"},"schema_version":"1.0"},"canonical_sha256":"83d044a8d167e5f1bb51b36d237fed33c735ce61c0850dd30512eee951d77ab7","source":{"kind":"arxiv","id":"1308.2858","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2858","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2858v2","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2858","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"QPIEJKGRM7S7","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QPIEJKGRM7S7DO2R","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QPIEJKGR","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QPIEJKGRM7S7DO2RWNWSG77NGP","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2858","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-13T13:22:02Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"33cc7e9a94d00e541e9d64f6004a3a4ab5d0a25fece9bc588201d249aa6baf36","abstract_canon_sha256":"1e30319d31f242515d7080555fd42d5d42e114c63e220b020fd42b32fbe71b28"},"schema_version":"1.0"},"canonical_sha256":"83d044a8d167e5f1bb51b36d237fed33c735ce61c0850dd30512eee951d77ab7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:57.077861Z","signature_b64":"/r1FUe2oTxATw5L3IK3gkTYcols/fNv56pwmcTw1fuo9mSsaljSjtFB64hLo3SIdgZ8ASNCNa6aNFaSWW9tnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83d044a8d167e5f1bb51b36d237fed33c735ce61c0850dd30512eee951d77ab7","last_reissued_at":"2026-05-18T03:15:57.077200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:57.077200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2858","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNaJF2hnameJub3t6zQYHLezTnqjoYyt5nWBvA98ow5ADgsCf6Iz9/Bk6aa80stiv39OrXEjU7Dar6eXIoB8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:14:52.496655Z"},"content_sha256":"139fe6d0096207734604da2af4cd0614ef3d32c136bc91fcee4f0d96c48a03f4","schema_version":"1.0","event_id":"sha256:139fe6d0096207734604da2af4cd0614ef3d32c136bc91fcee4f0d96c48a03f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QPIEJKGRM7S7DO2RWNWSG77NGP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameterized Algorithms for Modular-Width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"cs.DS","authors_text":"Jakub Gajarsk\\'y, Michael Lampis, Sebastian Ordyniak","submitted_at":"2013-08-13T13:22:02Z","abstract_excerpt":"It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as possible, covers dense graphs but does not incur such a heavy algorithmic penalty.\n  The main contribution of this paper is to consider a parameter called modular-width, defined using the well-known notion of modular decompositions. Using a combination of ILPs and dynamic programming we manage to design FPT algorithms for Coloring and Partitioning into paths "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2858","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkcL8Naq8Ty+1S9FW66N1h8i5OTiI7TnOI2cs6Fh2Szd8Gw3AVg+NJjqdBL5wMJ0qOGnpjt8ng48XZfbZgB1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:14:52.497331Z"},"content_sha256":"fdd7a28c2f57b1463f48fb681115244d34d7687217d5f33545689af544696dd9","schema_version":"1.0","event_id":"sha256:fdd7a28c2f57b1463f48fb681115244d34d7687217d5f33545689af544696dd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPIEJKGRM7S7DO2RWNWSG77NGP/bundle.json","state_url":"https://pith.science/pith/QPIEJKGRM7S7DO2RWNWSG77NGP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPIEJKGRM7S7DO2RWNWSG77NGP/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":"2026-06-10T00:14:52Z","links":{"resolver":"https://pith.science/pith/QPIEJKGRM7S7DO2RWNWSG77NGP","bundle":"https://pith.science/pith/QPIEJKGRM7S7DO2RWNWSG77NGP/bundle.json","state":"https://pith.science/pith/QPIEJKGRM7S7DO2RWNWSG77NGP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPIEJKGRM7S7DO2RWNWSG77NGP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QPIEJKGRM7S7DO2RWNWSG77NGP","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":"1e30319d31f242515d7080555fd42d5d42e114c63e220b020fd42b32fbe71b28","cross_cats_sorted":["cs.CC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-13T13:22:02Z","title_canon_sha256":"33cc7e9a94d00e541e9d64f6004a3a4ab5d0a25fece9bc588201d249aa6baf36"},"schema_version":"1.0","source":{"id":"1308.2858","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2858","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2858v2","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2858","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"QPIEJKGRM7S7","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QPIEJKGRM7S7DO2R","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QPIEJKGR","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:fdd7a28c2f57b1463f48fb681115244d34d7687217d5f33545689af544696dd9","target":"graph","created_at":"2026-05-18T03:15:57Z","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":"It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as possible, covers dense graphs but does not incur such a heavy algorithmic penalty.\n  The main contribution of this paper is to consider a parameter called modular-width, defined using the well-known notion of modular decompositions. Using a combination of ILPs and dynamic programming we manage to design FPT algorithms for Coloring and Partitioning into paths ","authors_text":"Jakub Gajarsk\\'y, Michael Lampis, Sebastian Ordyniak","cross_cats":["cs.CC","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-13T13:22:02Z","title":"Parameterized Algorithms for Modular-Width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2858","kind":"arxiv","version":2},"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":"sha256:139fe6d0096207734604da2af4cd0614ef3d32c136bc91fcee4f0d96c48a03f4","target":"record","created_at":"2026-05-18T03:15:57Z","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":"1e30319d31f242515d7080555fd42d5d42e114c63e220b020fd42b32fbe71b28","cross_cats_sorted":["cs.CC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-13T13:22:02Z","title_canon_sha256":"33cc7e9a94d00e541e9d64f6004a3a4ab5d0a25fece9bc588201d249aa6baf36"},"schema_version":"1.0","source":{"id":"1308.2858","kind":"arxiv","version":2}},"canonical_sha256":"83d044a8d167e5f1bb51b36d237fed33c735ce61c0850dd30512eee951d77ab7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83d044a8d167e5f1bb51b36d237fed33c735ce61c0850dd30512eee951d77ab7","first_computed_at":"2026-05-18T03:15:57.077200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:57.077200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/r1FUe2oTxATw5L3IK3gkTYcols/fNv56pwmcTw1fuo9mSsaljSjtFB64hLo3SIdgZ8ASNCNa6aNFaSWW9tnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:57.077861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2858","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:139fe6d0096207734604da2af4cd0614ef3d32c136bc91fcee4f0d96c48a03f4","sha256:fdd7a28c2f57b1463f48fb681115244d34d7687217d5f33545689af544696dd9"],"state_sha256":"3986dfbfdbc3054bf021135a6bf4aa0b2728310830d4fa76ef4559142f1e625f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HbnHHbIQwN4fMZWOjJM6hf90DhTEnCzwzZmgCn+7DtU3RRk+thxMZDV9MPgZOVnCPt6oRJOXhnsov9PBi07gBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:14:52.501682Z","bundle_sha256":"d6a378bf0cd75136eed4e71e7bcc7f8e31f81dcdaa9f259972e8c813dd4f75cb"}}