{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7D42BBDXPTJCU4E7L2I6NJD44X","short_pith_number":"pith:7D42BBDX","schema_version":"1.0","canonical_sha256":"f8f9a084777cd22a709f5e91e6a47ce5d4bac65f6ea7ba46704fb1ad1b0faf5b","source":{"kind":"arxiv","id":"1907.08906","version":1},"attestation_state":"computed","paper":{"title":"A Constant Approximation for Colorful k-Center","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Kasturi Varadarajan, Sayan Bandyapadhyay, Shreyas Pai, Tanmay Inamdar","submitted_at":"2019-07-21T03:53:54Z","abstract_excerpt":"In this paper, we consider the colorful $k$-center problem, which is a generalization of the well-known $k$-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius $\\rho$, such that with $k$ balls of radius $\\rho$, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a \"pseudo-approximation\" algorithm that works in any metric space, and an approximation algorithm that works for a"},"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":"1907.08906","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-07-21T03:53:54Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"51999effca553d0adde351d6ebefb15b308ceb8f08bf407a0c4f063ee5ccf419","abstract_canon_sha256":"4fbc8c630ab6d6920e111f362655140c7701976f7dfe205e58ff1895a26e7df5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:02.749912Z","signature_b64":"oD0TCiyrvBf1Br1AcG9JqpVdL1c47B8LgooEmUIzxIizQlfo1SQpM2AwuULfuNCh7LsjeDeo+PgC89pBDsvdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8f9a084777cd22a709f5e91e6a47ce5d4bac65f6ea7ba46704fb1ad1b0faf5b","last_reissued_at":"2026-05-17T23:40:02.749443Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:02.749443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Constant Approximation for Colorful k-Center","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Kasturi Varadarajan, Sayan Bandyapadhyay, Shreyas Pai, Tanmay Inamdar","submitted_at":"2019-07-21T03:53:54Z","abstract_excerpt":"In this paper, we consider the colorful $k$-center problem, which is a generalization of the well-known $k$-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius $\\rho$, such that with $k$ balls of radius $\\rho$, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a \"pseudo-approximation\" algorithm that works in any metric space, and an approximation algorithm that works for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08906","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.08906","created_at":"2026-05-17T23:40:02.749508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.08906v1","created_at":"2026-05-17T23:40:02.749508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08906","created_at":"2026-05-17T23:40:02.749508+00:00"},{"alias_kind":"pith_short_12","alias_value":"7D42BBDXPTJC","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7D42BBDXPTJCU4E7","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7D42BBDX","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X","json":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X.json","graph_json":"https://pith.science/api/pith-number/7D42BBDXPTJCU4E7L2I6NJD44X/graph.json","events_json":"https://pith.science/api/pith-number/7D42BBDXPTJCU4E7L2I6NJD44X/events.json","paper":"https://pith.science/paper/7D42BBDX"},"agent_actions":{"view_html":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X","download_json":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X.json","view_paper":"https://pith.science/paper/7D42BBDX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.08906&json=true","fetch_graph":"https://pith.science/api/pith-number/7D42BBDXPTJCU4E7L2I6NJD44X/graph.json","fetch_events":"https://pith.science/api/pith-number/7D42BBDXPTJCU4E7L2I6NJD44X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X/action/storage_attestation","attest_author":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X/action/author_attestation","sign_citation":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X/action/citation_signature","submit_replication":"https://pith.science/pith/7D42BBDXPTJCU4E7L2I6NJD44X/action/replication_record"}},"created_at":"2026-05-17T23:40:02.749508+00:00","updated_at":"2026-05-17T23:40:02.749508+00:00"}