{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UWX4RPCKX345LSSJMXOLJY33HE","short_pith_number":"pith:UWX4RPCK","canonical_record":{"source":{"id":"1107.2443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T00:51:53Z","cross_cats_sorted":["cs.DC","cs.SI"],"title_canon_sha256":"577b3f5e58a7d6680a329a9be9a7f7758e7ffa8db2bcf8f1f78c9b08e5475002","abstract_canon_sha256":"8ce79aa86a63fce91e9f65f54e479d07b4ffac2b8a7e1cf03b47258514608ed0"},"schema_version":"1.0"},"canonical_sha256":"a5afc8bc4abef9d5ca4965dcb4e37b39076a97b19094d134e4cad9e828546b12","source":{"kind":"arxiv","id":"1107.2443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2443","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2443v1","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2443","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"UWX4RPCKX345","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UWX4RPCKX345LSSJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UWX4RPCK","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UWX4RPCKX345LSSJMXOLJY33HE","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T00:51:53Z","cross_cats_sorted":["cs.DC","cs.SI"],"title_canon_sha256":"577b3f5e58a7d6680a329a9be9a7f7758e7ffa8db2bcf8f1f78c9b08e5475002","abstract_canon_sha256":"8ce79aa86a63fce91e9f65f54e479d07b4ffac2b8a7e1cf03b47258514608ed0"},"schema_version":"1.0"},"canonical_sha256":"a5afc8bc4abef9d5ca4965dcb4e37b39076a97b19094d134e4cad9e828546b12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:57.796294Z","signature_b64":"mi+ZLHb647rkcYEbeDQs3eCGFbY4hgypwyWvKvqhXDQ/6Vo+fyz3YhiCLTb9zbVr2hBuO5Pg7AJe34n8r/PMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5afc8bc4abef9d5ca4965dcb4e37b39076a97b19094d134e4cad9e828546b12","last_reissued_at":"2026-05-18T00:56:57.795592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:57.795592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2443","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XVePh5M5xORuPyuQKPyUGTuAXXaDJxeNPyn0gl6qKGkhQDFpyT4S8aF46iu3w/gUVfAieQSMTE+j/Ynu+rTOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:22:19.068686Z"},"content_sha256":"aa8c7b54a65de8ffe01d2fcac899432dfb23cc4678f5ee01361a919d66428e08","schema_version":"1.0","event_id":"sha256:aa8c7b54a65de8ffe01d2fcac899432dfb23cc4678f5ee01361a919d66428e08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UWX4RPCKX345LSSJMXOLJY33HE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Approximability and Hardness of Minimum Topic Connected Overlay and Its Special Instances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.SI"],"primary_cat":"cs.DS","authors_text":"Horotaka Ono, Jun Hosoda, Juraj Hromkovic, Koichi Wada, Monika Steinova, Taisuke Izumi","submitted_at":"2011-07-13T00:51:53Z","abstract_excerpt":"In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics and a collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(log t) in polynomial time. In this paper, we further investigate the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2443","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pfsNd6JJk+PCVcxkj6Q+zd7jGNxH+opd+6Ckc86eiGf2lSz3f/5nTKB4L3SR5UZeevfrT/879vAQ1+Wg/WBYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:22:19.069408Z"},"content_sha256":"eb68c8b6dc25c1b925c6ac9a1ad343038b5dc91cfb8ed606cde1d07635b99383","schema_version":"1.0","event_id":"sha256:eb68c8b6dc25c1b925c6ac9a1ad343038b5dc91cfb8ed606cde1d07635b99383"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UWX4RPCKX345LSSJMXOLJY33HE/bundle.json","state_url":"https://pith.science/pith/UWX4RPCKX345LSSJMXOLJY33HE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UWX4RPCKX345LSSJMXOLJY33HE/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":"2026-05-26T14:22:19Z","links":{"resolver":"https://pith.science/pith/UWX4RPCKX345LSSJMXOLJY33HE","bundle":"https://pith.science/pith/UWX4RPCKX345LSSJMXOLJY33HE/bundle.json","state":"https://pith.science/pith/UWX4RPCKX345LSSJMXOLJY33HE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UWX4RPCKX345LSSJMXOLJY33HE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UWX4RPCKX345LSSJMXOLJY33HE","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":"8ce79aa86a63fce91e9f65f54e479d07b4ffac2b8a7e1cf03b47258514608ed0","cross_cats_sorted":["cs.DC","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T00:51:53Z","title_canon_sha256":"577b3f5e58a7d6680a329a9be9a7f7758e7ffa8db2bcf8f1f78c9b08e5475002"},"schema_version":"1.0","source":{"id":"1107.2443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2443","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2443v1","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2443","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"UWX4RPCKX345","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UWX4RPCKX345LSSJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UWX4RPCK","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:eb68c8b6dc25c1b925c6ac9a1ad343038b5dc91cfb8ed606cde1d07635b99383","target":"graph","created_at":"2026-05-18T00:56:57Z","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":"In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics and a collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(log t) in polynomial time. In this paper, we further investigate the ","authors_text":"Horotaka Ono, Jun Hosoda, Juraj Hromkovic, Koichi Wada, Monika Steinova, Taisuke Izumi","cross_cats":["cs.DC","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T00:51:53Z","title":"On the Approximability and Hardness of Minimum Topic Connected Overlay and Its Special Instances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2443","kind":"arxiv","version":1},"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:aa8c7b54a65de8ffe01d2fcac899432dfb23cc4678f5ee01361a919d66428e08","target":"record","created_at":"2026-05-18T00:56:57Z","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":"8ce79aa86a63fce91e9f65f54e479d07b4ffac2b8a7e1cf03b47258514608ed0","cross_cats_sorted":["cs.DC","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T00:51:53Z","title_canon_sha256":"577b3f5e58a7d6680a329a9be9a7f7758e7ffa8db2bcf8f1f78c9b08e5475002"},"schema_version":"1.0","source":{"id":"1107.2443","kind":"arxiv","version":1}},"canonical_sha256":"a5afc8bc4abef9d5ca4965dcb4e37b39076a97b19094d134e4cad9e828546b12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5afc8bc4abef9d5ca4965dcb4e37b39076a97b19094d134e4cad9e828546b12","first_computed_at":"2026-05-18T00:56:57.795592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:57.795592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mi+ZLHb647rkcYEbeDQs3eCGFbY4hgypwyWvKvqhXDQ/6Vo+fyz3YhiCLTb9zbVr2hBuO5Pg7AJe34n8r/PMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:57.796294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa8c7b54a65de8ffe01d2fcac899432dfb23cc4678f5ee01361a919d66428e08","sha256:eb68c8b6dc25c1b925c6ac9a1ad343038b5dc91cfb8ed606cde1d07635b99383"],"state_sha256":"01c2d34773adf08f8efbfe79f901d771128cb9e687228acce73fb80e91c6a5ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xI4RxaALlq8raoRTwKmFARz/s1Wbhog85HH/aaUOq4M1j8f4FwqImCprMAV4xu4XeDaq1sclZFSgAPQbknGQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:22:19.073263Z","bundle_sha256":"20550816333ea864c9b0be90db2e875de43f24ddfad8a5aa163fc21b4fcf2e52"}}