{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EVLKGQEK76UUZYY5QA5DKCXHAR","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":"4239b60fa68bc233a136a2d82457741c76002730df91b69589230f7598b57496","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-22T16:57:49Z","title_canon_sha256":"162934102b2b89be06fa1ac50c762d2f8cd2c271f73c8028470a950a26e6b264"},"schema_version":"1.0","source":{"id":"1611.07414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07414","created_at":"2026-05-18T00:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07414v1","created_at":"2026-05-18T00:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07414","created_at":"2026-05-18T00:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"EVLKGQEK76UU","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EVLKGQEK76UUZYY5","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EVLKGQEK","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:9f2df2f2dbc685a9ec7a9855cf4b00b091f658168440ec88485ffbdab53a4c96","target":"graph","created_at":"2026-05-18T00:57:20Z","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 this paper we initiate the study of the heterogeneous capacitated $k$-center problem: given a metric space $X = (F \\cup C, d)$, and a collection of capacities. The goal is to open each capacity at a unique facility location in $F$, and also to assign clients to facilities so that the number of clients assigned to any facility is at most the capacity installed; the objective is then to minimize the maximum distance between a client and its assigned facility. If all the capacities $c_i$'s are identical, the problem becomes the well-studied uniform capacitated $k$-center problem for which cons","authors_text":"Amit Kumar, Deeparnab Chakrabarty, Ravishankar Krishnaswamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-22T16:57:49Z","title":"The Heterogeneous Capacitated $k$-Center Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07414","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:a87a2061518a9e0c8e8ef4649388d5c4065d1cb636a1402141a19be33f9479df","target":"record","created_at":"2026-05-18T00:57:20Z","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":"4239b60fa68bc233a136a2d82457741c76002730df91b69589230f7598b57496","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-22T16:57:49Z","title_canon_sha256":"162934102b2b89be06fa1ac50c762d2f8cd2c271f73c8028470a950a26e6b264"},"schema_version":"1.0","source":{"id":"1611.07414","kind":"arxiv","version":1}},"canonical_sha256":"2556a3408affa94ce31d803a350ae70443007f437867c9878240193f58830485","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2556a3408affa94ce31d803a350ae70443007f437867c9878240193f58830485","first_computed_at":"2026-05-18T00:57:20.180840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:20.180840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mjIM6gVM0xEVq/j+T7cXOQEk2FLLGZOzaj7YUoGzd1pYPNiyiN/JJBU6sM8BqelK/MEJIimWg/lbVRd9KkKOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:20.181383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a87a2061518a9e0c8e8ef4649388d5c4065d1cb636a1402141a19be33f9479df","sha256:9f2df2f2dbc685a9ec7a9855cf4b00b091f658168440ec88485ffbdab53a4c96"],"state_sha256":"8bd11644129c0b98dd3a99d0cfcdbeb9dfabab6bb9d9a62bd3644ed7e4f1e515"}