{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ATDFCRG6V2CHXRG3YHALACHDZM","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":"3682854949a46c95ef17eb04da6247587d8c285296a4e77e8420abe087390673","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-03-17T15:00:03Z","title_canon_sha256":"2d641f4d8a306e697522f964711afe9089dfca09a1c7596693dd1ec3dac524fa"},"schema_version":"1.0","source":{"id":"1703.06045","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06045","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06045v5","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06045","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"ATDFCRG6V2CH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"ATDFCRG6V2CHXRG3","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"ATDFCRG6","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:7731ae6ea961af7d50d632496b3592ca360d4b0b314cfc1a268acc7f39793c4c","target":"graph","created_at":"2026-05-18T00:36:03Z","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":"We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two. We then show that, in trees of height three, it is NP-hard to approximate the problem within a factor $2^{f(n)}$ for any sublinear function $f$ of the size of the input $n$. Again, this bound is tight, as we prove t","authors_text":"Cassio P. de Campos, Denis D. Mau\\'a, Diarmaid Conaty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-03-17T15:00:03Z","title":"Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06045","kind":"arxiv","version":5},"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":"sha256:2e99f763f06f1fe4d95b606781fdc233817bda798d0a41096d5ba62b39e3d87d","target":"record","created_at":"2026-05-18T00:36:03Z","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":"3682854949a46c95ef17eb04da6247587d8c285296a4e77e8420abe087390673","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-03-17T15:00:03Z","title_canon_sha256":"2d641f4d8a306e697522f964711afe9089dfca09a1c7596693dd1ec3dac524fa"},"schema_version":"1.0","source":{"id":"1703.06045","kind":"arxiv","version":5}},"canonical_sha256":"04c65144deae847bc4dbc1c0b008e3cb07f52dc91ab3149b10cd5b5af61c1b2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04c65144deae847bc4dbc1c0b008e3cb07f52dc91ab3149b10cd5b5af61c1b2b","first_computed_at":"2026-05-18T00:36:03.431008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:03.431008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FqeA5RFjglmsw9Hhi4sIEgYkjh7W1WrQKbwjCjCsIjJJkNZEbfIoVZoVMOxjSqi85EfbZ15Pr1sTST3e0xe8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:03.431448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06045","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e99f763f06f1fe4d95b606781fdc233817bda798d0a41096d5ba62b39e3d87d","sha256:7731ae6ea961af7d50d632496b3592ca360d4b0b314cfc1a268acc7f39793c4c"],"state_sha256":"fd8dc3466881fe2589f0930a594fea6c22cca2f29ba900f600392876e23f500c"}