{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RHM7CAB4NJTLAPGA743CK6OECT","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":"27ce8affb4ab7e699fd7b4c7a841ab8fa34bda3a09e97d00404d7377ae515aa9","cross_cats_sorted":["cs.IR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-08T12:51:03Z","title_canon_sha256":"44f88b7d5929b9b92af9f9182822691764572286024f69b8185cf64faccc0ee7"},"schema_version":"1.0","source":{"id":"1007.1361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1361","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1361v2","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1361","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"RHM7CAB4NJTL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RHM7CAB4NJTLAPGA","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RHM7CAB4","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:f1b4f40b24c800f4d77496808c9bbd83d74e08206975e325557d51e1dfa78cf7","target":"graph","created_at":"2026-05-18T04:39:09Z","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":"In this paper we describe a new efficient (in fact optimal) data structure for the {\\em top-$K$ color problem}. Each element of an array $A$ is assigned a color $c$ with priority $p(c)$. For a query range $[a,b]$ and a value $K$, we have to report $K$ colors with the highest priorities among all colors that occur in $A[a..b]$, sorted in reverse order by their priorities. We show that such queries can be answered in $O(K)$ time using an $O(N\\log \\sigma)$ bits data structure, where $N$ is the number of elements in the array and $\\sigma$ is the number of colors. Thus our data structure is asympto","authors_text":"Marek Karpinski, Yakov Nekrich","cross_cats":["cs.IR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-08T12:51:03Z","title":"Top-K Color Queries for Document Retrieval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1361","kind":"arxiv","version":2},"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":"sha256:45a74fce1e029139e02b953b4396d44eac29297d9bbb356c6fd715f032f33aab","target":"record","created_at":"2026-05-18T04:39:09Z","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":"27ce8affb4ab7e699fd7b4c7a841ab8fa34bda3a09e97d00404d7377ae515aa9","cross_cats_sorted":["cs.IR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-08T12:51:03Z","title_canon_sha256":"44f88b7d5929b9b92af9f9182822691764572286024f69b8185cf64faccc0ee7"},"schema_version":"1.0","source":{"id":"1007.1361","kind":"arxiv","version":2}},"canonical_sha256":"89d9f1003c6a66b03cc0ff362579c414c465b1d7c3bab1fcce3c4882ec714332","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89d9f1003c6a66b03cc0ff362579c414c465b1d7c3bab1fcce3c4882ec714332","first_computed_at":"2026-05-18T04:39:09.925781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:09.925781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53mUhYVQBUNml1K8Po9yv/ja6dEn2EM2gFLPkAxGEL8Ye9Zux/Lxcah7P01xY1KfAxzyQj2P9EmxBu/45CxiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:09.926224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45a74fce1e029139e02b953b4396d44eac29297d9bbb356c6fd715f032f33aab","sha256:f1b4f40b24c800f4d77496808c9bbd83d74e08206975e325557d51e1dfa78cf7"],"state_sha256":"7259daf284b71b08d537285ac49736d1968e2e5758ae0d6efc524c0675ea5d3f"}