{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7NPQ534EWA4RODPSNSFMG2KQM2","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":"d4e5216c03d6fb9f8e4fde500716d7bf42f6c84d12c442e6d9c18cc094ed96d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-27T11:09:37Z","title_canon_sha256":"36cff482aeb2af097b00edf339a367c1174e0b4877094f043c9ebe2a6e96424b"},"schema_version":"1.0","source":{"id":"1312.7243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7243","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7243v2","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7243","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"7NPQ534EWA4R","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7NPQ534EWA4RODPS","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7NPQ534E","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:88677ee9e3468ec27f2397aad83241dfb257555280c06e11ec412fccb69e8e87","target":"graph","created_at":"2026-05-18T03:03:12Z","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 article, we consider the problem of computing minimum dominating set for a given set $S$ of $n$ points in $\\IR^2$. Here the objective is to find a minimum cardinality subset $S'$ of $S$ such that the union of the unit radius disks centered at the points in $S'$ covers all the points in $S$. We first propose a simple 4-factor and 3-factor approximation algorithms in $O(n^6 \\log n)$ and $O(n^{11} \\log n)$ time respectively improving time complexities by a factor of $O(n^2)$ and $O(n^4)$ respectively over the best known result available in the literature [M. De, G.K. Das, P. Carmi and S.C","authors_text":"Gautam K. Das, Prajwal R. Prasad, Ramesh K. Jallu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-27T11:09:37Z","title":"Minimum Dominating Set for a Point Set in $\\IR^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7243","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:f62e80923d945d9d62ae3c9d4902f33815d7ca436f736ddf8c58393aafee92d9","target":"record","created_at":"2026-05-18T03:03:12Z","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":"d4e5216c03d6fb9f8e4fde500716d7bf42f6c84d12c442e6d9c18cc094ed96d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-27T11:09:37Z","title_canon_sha256":"36cff482aeb2af097b00edf339a367c1174e0b4877094f043c9ebe2a6e96424b"},"schema_version":"1.0","source":{"id":"1312.7243","kind":"arxiv","version":2}},"canonical_sha256":"fb5f0eef84b039170df26c8ac369506690d5ce002a8fdfe15cd904c9ab0d0abd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb5f0eef84b039170df26c8ac369506690d5ce002a8fdfe15cd904c9ab0d0abd","first_computed_at":"2026-05-18T03:03:12.232857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:12.232857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BhDUFb2hXetZPlBItUCLsANYlAiu7GU7EShbKf2eNYOsRjjvAFmpGbdTpHvWuOphdT5GoENsxPboJGBd38s2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:12.233544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f62e80923d945d9d62ae3c9d4902f33815d7ca436f736ddf8c58393aafee92d9","sha256:88677ee9e3468ec27f2397aad83241dfb257555280c06e11ec412fccb69e8e87"],"state_sha256":"5bb13381b6101416b7e5c91cb2814b086ed355348c91ba8f4248669af37a1cd3"}