{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OZEDKLT4KF4Z54NRGVIRZS2ADC","short_pith_number":"pith:OZEDKLT4","schema_version":"1.0","canonical_sha256":"7648352e7c51799ef1b135511ccb4018ab3b0d99fbf6b272595169f22abe9a30","source":{"kind":"arxiv","id":"1510.05886","version":2},"attestation_state":"computed","paper":{"title":"Approximation Algorithm for Minimum Weight Connected $m$-Fold Dominating Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Ding-Zhu Du, Jiao Zhou, Ker-I Ko, Zhao Zhang","submitted_at":"2015-10-20T13:32:28Z","abstract_excerpt":"Using connected dominating set (CDS) to serve as a virtual backbone in a wireless networks can save energy and reduce interference. Since nodes may fail due to accidental damage or energy depletion, it is desirable that the virtual backbone has some fault-tolerance. A $k$-connected $m$-fold dominating set ($(k,m)$-CDS) of a graph $G$ is a node set $D$ such that every node in $V\\setminus D$ has at least $m$ neighbors in $D$ and the subgraph of $G$ induced by $D$ is $k$-connected. Using $(k,m)$-CDS can tolerate the failure of $\\min\\{k-1,m-1\\}$ nodes. In this paper, we study Minimum Weight $(1,m)"},"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":"1510.05886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-10-20T13:32:28Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"6355b6aebb1c20051dce544b4f60dbf0e4df9a32d3a8de71bc119cb10714435a","abstract_canon_sha256":"8c1179c5ba0c732496cce352f286ab9f3f065f6242d10ae855794340cbea4433"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:54.894136Z","signature_b64":"kYc/YRA5FI5tHdWLR5LC9MKdi6wZ2z6q9anoyMv82Htr+BC0ibtGZOx48ipevyz4Ts/Hs+U4+8taOvscwZpwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7648352e7c51799ef1b135511ccb4018ab3b0d99fbf6b272595169f22abe9a30","last_reissued_at":"2026-05-18T00:48:54.893292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:54.893292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation Algorithm for Minimum Weight Connected $m$-Fold Dominating Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Ding-Zhu Du, Jiao Zhou, Ker-I Ko, Zhao Zhang","submitted_at":"2015-10-20T13:32:28Z","abstract_excerpt":"Using connected dominating set (CDS) to serve as a virtual backbone in a wireless networks can save energy and reduce interference. Since nodes may fail due to accidental damage or energy depletion, it is desirable that the virtual backbone has some fault-tolerance. A $k$-connected $m$-fold dominating set ($(k,m)$-CDS) of a graph $G$ is a node set $D$ such that every node in $V\\setminus D$ has at least $m$ neighbors in $D$ and the subgraph of $G$ induced by $D$ is $k$-connected. Using $(k,m)$-CDS can tolerate the failure of $\\min\\{k-1,m-1\\}$ nodes. In this paper, we study Minimum Weight $(1,m)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05886","kind":"arxiv","version":2},"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":"1510.05886","created_at":"2026-05-18T00:48:54.893448+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.05886v2","created_at":"2026-05-18T00:48:54.893448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05886","created_at":"2026-05-18T00:48:54.893448+00:00"},{"alias_kind":"pith_short_12","alias_value":"OZEDKLT4KF4Z","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OZEDKLT4KF4Z54NR","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OZEDKLT4","created_at":"2026-05-18T12:29:34.919912+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/OZEDKLT4KF4Z54NRGVIRZS2ADC","json":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC.json","graph_json":"https://pith.science/api/pith-number/OZEDKLT4KF4Z54NRGVIRZS2ADC/graph.json","events_json":"https://pith.science/api/pith-number/OZEDKLT4KF4Z54NRGVIRZS2ADC/events.json","paper":"https://pith.science/paper/OZEDKLT4"},"agent_actions":{"view_html":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC","download_json":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC.json","view_paper":"https://pith.science/paper/OZEDKLT4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.05886&json=true","fetch_graph":"https://pith.science/api/pith-number/OZEDKLT4KF4Z54NRGVIRZS2ADC/graph.json","fetch_events":"https://pith.science/api/pith-number/OZEDKLT4KF4Z54NRGVIRZS2ADC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC/action/storage_attestation","attest_author":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC/action/author_attestation","sign_citation":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC/action/citation_signature","submit_replication":"https://pith.science/pith/OZEDKLT4KF4Z54NRGVIRZS2ADC/action/replication_record"}},"created_at":"2026-05-18T00:48:54.893448+00:00","updated_at":"2026-05-18T00:48:54.893448+00:00"}