{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OIUYXTUKMFAEPRS25SMY4YDTW5","short_pith_number":"pith:OIUYXTUK","schema_version":"1.0","canonical_sha256":"72298bce8a614047c65aec998e6073b77f208a5b373b58204cd5caba1eb7a5b7","source":{"kind":"arxiv","id":"2506.13191","version":1},"attestation_state":"computed","paper":{"title":"FPT Constant Approximation Algorithms for Colorful Sum of Radii","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Gregory Gutin, Shuilian Liu, Yicheng Xu, Yong Zhang","submitted_at":"2025-06-16T07:59:42Z","abstract_excerpt":"We study the colorful sum of radii problem, where the input is a point set $P$ partitioned into classes $P_1, P_2, \\dots, P_\\omega$, along with per-class outlier bounds $m_1, m_2, \\dots, m_\\omega$, summing to $m$. The goal is to select a subset $\\mathcal{C} \\subseteq P$ of $k$ centers and assign points to centers in $\\mathcal{C}$, allowing up to $m_i$ unassigned points (outliers) from each class $P_i$, while minimizing the sum of cluster radii. The radius of a cluster is defined as the maximum distance from any point in the cluster to its center. The classical (non-colorful) version of the sum"},"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":"2506.13191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-16T07:59:42Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"6d76042bbae53957e81b12d52fd9cfa6d314550b25eccd26c818692142316a12","abstract_canon_sha256":"8025f820edc403147fdc9dff645d8728df10af066ce98d140d6585c31377638b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:06.536106Z","signature_b64":"xhQ59F/DiYWzKH4NHnCJJfvkZQsuBRMluP+W9amyxFGt+PpjT3QfKSNhwE2aSx9GGlApT+5zW4SGhwJOr9ghCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72298bce8a614047c65aec998e6073b77f208a5b373b58204cd5caba1eb7a5b7","last_reissued_at":"2026-07-05T11:22:06.535683Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:06.535683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"FPT Constant Approximation Algorithms for Colorful Sum of Radii","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Gregory Gutin, Shuilian Liu, Yicheng Xu, Yong Zhang","submitted_at":"2025-06-16T07:59:42Z","abstract_excerpt":"We study the colorful sum of radii problem, where the input is a point set $P$ partitioned into classes $P_1, P_2, \\dots, P_\\omega$, along with per-class outlier bounds $m_1, m_2, \\dots, m_\\omega$, summing to $m$. The goal is to select a subset $\\mathcal{C} \\subseteq P$ of $k$ centers and assign points to centers in $\\mathcal{C}$, allowing up to $m_i$ unassigned points (outliers) from each class $P_i$, while minimizing the sum of cluster radii. The radius of a cluster is defined as the maximum distance from any point in the cluster to its center. The classical (non-colorful) version of the sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13191","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.13191/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.13191","created_at":"2026-07-05T11:22:06.535739+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.13191v1","created_at":"2026-07-05T11:22:06.535739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13191","created_at":"2026-07-05T11:22:06.535739+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIUYXTUKMFAE","created_at":"2026-07-05T11:22:06.535739+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIUYXTUKMFAEPRS2","created_at":"2026-07-05T11:22:06.535739+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIUYXTUK","created_at":"2026-07-05T11:22:06.535739+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2602.05476","citing_title":"FPT Approximations for Fair Sum of Radii with Outliers and General Norm Objectives","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06398","citing_title":"On the Parameterized Approximability of (Mergeable) Sum of Radii Clustering","ref_index":40,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5","json":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5.json","graph_json":"https://pith.science/api/pith-number/OIUYXTUKMFAEPRS25SMY4YDTW5/graph.json","events_json":"https://pith.science/api/pith-number/OIUYXTUKMFAEPRS25SMY4YDTW5/events.json","paper":"https://pith.science/paper/OIUYXTUK"},"agent_actions":{"view_html":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5","download_json":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5.json","view_paper":"https://pith.science/paper/OIUYXTUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.13191&json=true","fetch_graph":"https://pith.science/api/pith-number/OIUYXTUKMFAEPRS25SMY4YDTW5/graph.json","fetch_events":"https://pith.science/api/pith-number/OIUYXTUKMFAEPRS25SMY4YDTW5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5/action/storage_attestation","attest_author":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5/action/author_attestation","sign_citation":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5/action/citation_signature","submit_replication":"https://pith.science/pith/OIUYXTUKMFAEPRS25SMY4YDTW5/action/replication_record"}},"created_at":"2026-07-05T11:22:06.535739+00:00","updated_at":"2026-07-05T11:22:06.535739+00:00"}