{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:46YOFCPWRRZIUWOFCDVPXD6IUP","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":"57dd4a4bc79a6f97ea2d95c8d8f6d04752617534d2be4937d611ee6e6f4f6480","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T00:09:23Z","title_canon_sha256":"2596224293182828cc7393e2a07e80db52be6048cd62fb881d0d3da07e0fe77d"},"schema_version":"1.0","source":{"id":"1502.07406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07406","created_at":"2026-05-18T02:26:09Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07406v1","created_at":"2026-05-18T02:26:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07406","created_at":"2026-05-18T02:26:09Z"},{"alias_kind":"pith_short_12","alias_value":"46YOFCPWRRZI","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"46YOFCPWRRZIUWOF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"46YOFCPW","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:dc76343a67cd3f2018dab69755737769ed19ed78bc337d83ca79825e49defe2a","target":"graph","created_at":"2026-05-18T02:26:09Z","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":"This paper presents a polynomial-time $1/2$-approximation algorithm for maximizing nonnegative $k$-submodular functions. This improves upon the previous $\\max\\{1/3, 1/(1+a)\\}$-approximation by Ward and \\v{Z}ivn\\'y~(SODA'14), where $a=\\max\\{1, \\sqrt{(k-1)/4}\\}$. We also show that for monotone $k$-submodular functions there is a polynomial-time $k/(2k-1)$-approximation algorithm while for any $\\varepsilon>0$ a $((k+1)/2k+\\varepsilon)$-approximation algorithm for maximizing monotone $k$-submodular functions would require exponentially many queries. In particular, our hardness result implies that ","authors_text":"Satoru Iwata, Shin-ichi Tanigawa, Yuichi Yoshida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T00:09:23Z","title":"Improved Approximation Algorithms for k-Submodular Function Maximization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07406","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":"sha256:6c87403f47a4f96c2631f10a565c82049ccd019b663691719b89982a3eed4a4f","target":"record","created_at":"2026-05-18T02:26:09Z","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":"57dd4a4bc79a6f97ea2d95c8d8f6d04752617534d2be4937d611ee6e6f4f6480","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T00:09:23Z","title_canon_sha256":"2596224293182828cc7393e2a07e80db52be6048cd62fb881d0d3da07e0fe77d"},"schema_version":"1.0","source":{"id":"1502.07406","kind":"arxiv","version":1}},"canonical_sha256":"e7b0e289f68c728a59c510eafb8fc8a3c70bf4ac3da1f38fad6b3a6dbfcf3156","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7b0e289f68c728a59c510eafb8fc8a3c70bf4ac3da1f38fad6b3a6dbfcf3156","first_computed_at":"2026-05-18T02:26:09.880134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:09.880134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dzboBIpZck0OKmo+ouV3DWRWUqCUaDvEnY6kwuBIpKVjCxuxHD7QVNRxphJmU+emeGYiYvOZgmaACjkBXGATBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:09.880854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c87403f47a4f96c2631f10a565c82049ccd019b663691719b89982a3eed4a4f","sha256:dc76343a67cd3f2018dab69755737769ed19ed78bc337d83ca79825e49defe2a"],"state_sha256":"410b683c5776852a14b7dd823ec99f3f4d8832f74d67009faa3b4b36691fa408"}