{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:J5I2ONZHCWRNVKGLHWLRPTNKIO","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":"ab68ad1cb48d77734709269213608e441b5ee68b2270cb27cdc6237bcc5026a5","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-11T17:51:23Z","title_canon_sha256":"1ec03e08230a62d559d8ae73174cd91fd2f81af75cdeba770294ac5215ca8c7a"},"schema_version":"1.0","source":{"id":"1707.03387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03387","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03387v1","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03387","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"J5I2ONZHCWRN","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J5I2ONZHCWRNVKGL","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J5I2ONZH","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:12618c04576235050d6143d16006c2681143a506317f47d4563bb21e040658ae","target":"graph","created_at":"2026-05-18T00:40:29Z","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":"The minimum $k$-enclosing ball problem seeks the ball with smallest radius that contains at least~$k$ of~$m$ given points in a general $n$-dimensional Euclidean space. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of~$k$ points to solve this problem. The nodes on the tree are ordered in a suitable way, which, complemented with a last-in-first-out search strategy, allows for only a small fraction of nodes to be explored. Additionally, an efficient dual algorithm to solve the subproblems at each node is employed.","authors_text":"Farid Alizadeh, Marta Cavaleiro","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-11T17:51:23Z","title":"A branch-and-bound algorithm for the minimum radius $k$-enclosing ball problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03387","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:f2f795faea46a82867b76acfb75d56b25eb56d399c3ee2a5a7b446379b895e96","target":"record","created_at":"2026-05-18T00:40:29Z","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":"ab68ad1cb48d77734709269213608e441b5ee68b2270cb27cdc6237bcc5026a5","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-11T17:51:23Z","title_canon_sha256":"1ec03e08230a62d559d8ae73174cd91fd2f81af75cdeba770294ac5215ca8c7a"},"schema_version":"1.0","source":{"id":"1707.03387","kind":"arxiv","version":1}},"canonical_sha256":"4f51a7372715a2daa8cb3d9717cdaa43a7be7a81515c51d496131b8f7cf18a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f51a7372715a2daa8cb3d9717cdaa43a7be7a81515c51d496131b8f7cf18a43","first_computed_at":"2026-05-18T00:40:29.182285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:29.182285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tGFGDvNywFc43iA4mFo1ioN2LpffbGYSZYD24Jfi1vLAsy8Fo5w2Z4VSu7MiQxG3idsW9Miw3efbRKHiHgbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:29.182950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2f795faea46a82867b76acfb75d56b25eb56d399c3ee2a5a7b446379b895e96","sha256:12618c04576235050d6143d16006c2681143a506317f47d4563bb21e040658ae"],"state_sha256":"3c019bfd9e9c6d4e7f8a75b3561dbca6d65728d96484e09b21f5e66d5715ff38"}